LIBRARY 

OK   THK 

UNIVERSITY  OF  CALIFORNIA. 


Accession 


SMITHSONIAN    CONTRIBUTIONS   TO    KNOWLEDGE. 
801 


EXPERIMENTS 


IN 


AERODYNAMICS. 


S.  P.  LANGLEY. 


SECOND   EDITION. 

(First  Edition  Published  in  1891.) 


CITY  OF  WASHINGTON  : 

PUBLISHED  BY  THE  SMITHSONIAN  INSTITUTION 

1902. 


v^ 

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0 


COMMISSION  TO  WHOM  THIS  MEMOIR  HAS  BEEN  REFERRED. 

Professor  SIMON  NEWCOMB,  U.  S.  N. 
Professor  HENRY  A.  ROWLAND. 
Professor  CLEVELAND  ABBE. 


.     s  t' 


(n) 


PREFACE  TO  THE  FIRST  EDITION. 

If  there  prove  to  be  anything  of  permanent  value  in  these  investigations,  I 
desire  that  they  may  be  remembered  in  connection  with  the  name  of  the  late 
William  Thaw,  whose  generosity  provided  the  principal  means  for  them. 

I  have  to  thank  the  board  of  direction  of  the  Bache  fund  of  the  National 
Academy  of  Sciences  for  their  aid,  and  also  the  trustees  of  the  Western  Uni- 
versity of  Pennsylvania  for  their  permission  to  use  the  means  of  the  observatory 
under  their  charge  in  contributing  to  the  same  end,  and  I  desire  to  acknowledge 
especially  the  constant  and  valued  help  of  Mr.  Frank  W.  Very,  who  has  assisted 
me  in  all  these  experiments,  and  my  further  obligation  to  Mr.  George  E.  Curtis, 
who  has  most  efficiently  aided  me  in  the  final  computations  and  reductions. 

S.  P.  LANGLEY. 

SMITHSONIAN  INSTITUTION, 

WASHINGTON,  1891. 


I  037 II 


PREFACE   TO   THE  SECOND  EDITION. 

The  first  edition  of  this  work  being  exhausted,  a  second  is  now  published, 
in  which,  however,  little  is  added  to  the  subject  matter  already  printed,  for 
though  a  description  of  the  construction  here  of  heavy  flying  machines  mostly 
built  of  steel,  which  have  flown  long  distances,  is  already  prepared,  it  has  not 
been  considered  best  to  publish  the  details  at  present.  In  the  meantime,  the 
fact  that  such  machines,  made  on  the  principles  and  in  the  light  of  the  experi- 
ments first  shown  in  this  book,  have  since  actually  flown  (See  Comptes  Rendus, 
t.  CXXII,  Sea  nee  2(5  Mai,  189(i;  Nature,  Vol.  54,  May  28,  1896,)  will  give,  it  is 
hoped,  an  additional  weight,  and  interest  to  the  statements  in  the  present 
volume. 

S.  P.  LANG  LEY. 
SMITHS* >MA x  I NSTITTTTION, 

WASHINGTON,  APIUL,  1902. 


CONTENTS. 


PREFACE 1 

CHAPTER       I. — Introductory • 3 

II. — Character  and  Method  of  Experiments 7 

III.— The  Suspended  Plane 12 

IV. — The  Resultant  Pressure  Recorder 15 

V.— The  Plane-Dropper 26 

VI. — The  Component  Pressure  Recorder 48 

VII. — The  Dynamometer-Chronograph 75 

VIII.— The  Counterpoised  Eccentric  Plane '. 89 

IX.— The  Rolling  Carriage 94 

X. — Summary 105 

Appendix  A 109 

Appendix  B 113 

Appendix  C 114 


(m) 


CHAPTER  I. 

INTRODUCTORY. 

Schemes  for  mechanical  flight  have  been  so  generally  associated  in  the  past 
with  other  methods  than  those  of  science,  that  it  is  commonly  supposed  the 
long  record  of  failures  has  left  such  practical  demonstration  of  the  futility  of  all 
such  hopes  for  the  future  that  no  one  of  scientific  training  will  be  found  to  give 
them  countenance.  While  recognizing  that  this  view  is  a  natural  one,  I  have, 
however,  during  some  years,  devoted  nearly  all  the  time  at  my  command  for 
research,  if  not  directly  to  this  purpose,  yet  to  one  cognate  to  it,  with  a  result 
which  I  feel  ought  now  to  be  made  public. 

To  prevent  misapprehension,  let  me  state  at  the  outset  that  I  do  not  undertake 
to  explain  any  art  of  mechanical  flight,  but  to  demonstrate  experimentally  certain 
propositions  in  aei-odynamics  which  prove  that  such  flight  under  proper  direction 
is  practicable.  This  being  understood,  I  may  state  that  these  researches  have 
led  to  the  result  that  mechanical  sustentation  of  heavy  bodies  in  the  air,  com- 
bined with  very  great  speeds,  is  not  only  possible,  but  within  the  reach  of  mechan- 
ical means  we  actually  possess,  and  that  while  these  researches  are,  as  I  have  said, 
not  meant  to  demonstrate  the  art  of  guiding  such  heavy  bodies  in  flight,  they  do 
show  that  we  now  have  the  power  to  sustain  and  propel  them. 

Further  than  this,  these  new  experiments,  (and  theory  also  when  reviewed 
in  their  light,)  show  that  if  in  such  aerial  motion,  there  be  given  a  plane  of  fixed 
size  and  weight,  inclined  at  such  an  angle,  and  moved  forward  at  such  a  speed, 
that  it  shall  be  sustained  in  horizontal  flight,  then  the  more  rapid  the  motion  is, 
the  less  will  be  the  power  required  to  support  and  advance  it.  This  statement 
may,  I  am  aware,  present  an  appearance  so  paradoxical  that  the  reader  may  ask 
himself  if  he  has  rightly  understood  it.  To  make  the  meaning  quite  indubitable, 
let  me  repeat  it  in  another  form,  and  say  that  these  experiments  show  that  a 
definite  amount  of  power  so  expended  at  any  constant  rate,  will  attain  more 
economical  results  at  high  speeds  than  at  low  ones — e.  g.,  one  horse-power  thus 
employed,  will  transport  a  larger  weight  at  20  miles  an  hour  than  at  10,  a  still 
larger  at  40  miles  than  at  20,  and  so  on,  with  an  increasing  economy  of  power 
with  each  higher  speed,  up  to  some  remote  limit  not  yet  attained  in  experiment, 
but  probably  represented  by  higher  speeds  than  have  as  yet  been  reached  in 
any  other  mode  of  transport — a  statement  which  demands  and  will  receive  the 
amplest  confirmation  later  in  these  pages. 


4  EXPERIMENTS    IN    AERODYNAMICS. 

I  have  now  been  engaged  since  the  beginning  of  the  year  1887  in  experiments 
on  an  extended  scale  for  determining  the  possibility  of,  and  the  conditions  for, 
transporting  in  the  air  a  body  whose  specific  gravity  is  greater  than  that  of  the 
air,  and  I  desire  to  repeat  my  conviction  that  the  obstacles  in  its  way  are  not 
such  as  have  been  thought  ;  that  they  lie  more  in  such  apparently  secondary 
difficulties  as  those  of  guiding  the  body  so  that  it  may  move  in  the  direction 
desired,  and  ascend  or  descend  with  safety,  than  in  what  may  appear  to  be  the 
primary  difficulties  due  to  the  nature  of  the  air  itself,  and  that  in  my  opinion 
the  evidence  for  this  is  now  sufficiently  complete  to  engage  the  serious  attention 
of  engineers  to  the  practical  solution  of  these  secondary  difficulties,  and  to  the 
development  of  an  art  of  mechanical  flight  which  will  bring  with  it  a  change  in 
many  of  the  conditions  of  individual  and  national  existence  whose  importance  can 
hardly  be  estimated. 

The  way  to  this  has  not  been  pointed  out  by  established  treatises  on  aero- 
dynamics, whose  fundamental  postulates,  like  those  of  any  other  established 
science,  may  be  held  to  contain  implicitly  all  truths  deducible  from  them,  but 
which  are  so  far  from  being  of  practical  help  here,  that  from  these  postulates 
previous  writers  of  the  highest  repute  have  deduced  the  directly  opposite  con- 
clusion, that  mechanical  flight  is  practically  impossible.*  Reason  unaided  by 
new  experiment,  then,  has  done  little  or  nothing  in  favor  of  the  view  now  taken. 

It  may  be  asked  whether  it  is  not  otherwise  with  statements  which  are 
authorized  by  such  names  as  that  of  Newton,  and  whether  a  knowledge  of  truths 
mathematically  deducible  from  them,  would  not  at  any  rate  furnish  a  test  to 
distinguish  the  probably  true  from  the  probably  false;  but  here  it  is  important 
to  remember  that  the  mathematical  method  as  applied  to  physics,  must  always 
be  trustworthy  or  untrustworthy,  according  to  the  trustworthiness  of  the  data 
which  are  employed ;  that  the  most  complete  presentation  of  symbols  and  pro- 
cesses will  only  serve  to  enlarge  the  consequence  of  error  hidden  in  the  original 
premises,  if  such  there  be,  and  that  here,  as  will  be  shown,  the  error  as  to  fact 
begins  with  the  great  name  of  Newton  himself. 

In  this  untrodden  field  of  research,  which  looks  to  mechanical  flight,  not  by 
means  of  balloons,  but  by  bodies  specifically  heavier  than  the  air  in  which  they 
move,  I  think  it  safe  to  say  that  we  are  still,  at  the  time  this  is  written,  in  a 
relatively  less  advanced  condition  than  the  study  of  steam  was  before  the  time 
of  Newcomen  ;  and  if  we  remember  that  such  statements  as  have  been  com- 
monly made  with  reference  to  this,  till  lately  are,  with  rare  exceptions,  the  product 
of  conjecture  rather  than  of  study  and  experiment,  we  may  better  see  that  there 
is  here  as  yet,  no  rule  to  distinguish  the  probably  important  from  the  probably 
unimportant,  such  as  we  command  in  publications  devoted  to  the  progress  of 
already  established  sciences. 

*See  paper  by  Gay-Lussac  and  Navier,  cited  later. 


INTRODUCTORY.  5 

There  is  an  excellent  custom  among  scientific  investigators,  of  prefacing  the 
account  of  each  new  research  with  an  abstract  of  the  work  of  those  who  have 
already  presumably  advanced  knowledge  in  the  science  in  question ;  but  in  this 
case,  where  almost  nothing  is  established,  I  have  found  hardly  any  test  but  that 
of  experiment  to  distinguish  between  those  suggestions  presumably  worth  citation 
and  attention  and  those  which  are  not.  Since,  then,  it  i.s  usually  only  after 
the  experiments  which  are  later  to  be  described  have  been  made,  that  we  can 
distinguish  in  retrospective  examination  what  would  have  been  useful  to  the 
investigator  if  he  could  have  appreciated  its  true  character  without  this  test,  I 
have  deferred  the  task  of  giving  a  -resume  of  the  literature  of  the  subject  until  it 
could  be  done  in  the  light  of  acquired  knowledge. 

I  have  thus  been  led  to  give  the  time  which  I  could  dispose  of,  so  exclusively 
to  experiment,  that  it  may  well  be  that  I  have  missed  the  knowledge  of  some 
recent  researches  of  value ;  and  if  this  be  so,  I  desire  that  the  absence  of  mention 
of  them  in  the  present  publication,  may  be  taken  as  the  result,  not  of  design,  but 
of  an  ignorance,  which  I  shall  hope,  in  such  case,  to  repair  in  a  later  publication  ; 
while,  among  the  few  earlier  memoirs  that  I  arn  conscious  of  owing  much  useful 
suggestion  to,  it  is  just  that  I  should  mention  a  remarkable  one  by  Mr.  Wenham, 
which  appeared  in  the  first  number  of  the  London  Aeronautical  Society's  report, 
24  years  ago,  and  some  by  Penaud  in  L1  Aeronaute. 

The  reader,  especially  if  he  be  himself  skilled  in  observation,  may  perhaps 
be  willing  to  agree  that  since  there  is  here  so  little  yet  established,  so  great  a 
variety  of  tentative  experiments  must  be  made,  that  it  is  impossible  to  give  each 
of  them  at  the  outset  all  the  degree  of  accuracy  which  is  ultimately  desirable,  and 
that  he  may  yet  find  all  trustworthy  within  the  limits  of  their  present  application. 

I  do  not,  then,  offer  here  a  treatise  on  aerodynamics,  but  an  experimental 
demonstration  that  we  already  possess  in  the  steam-engine  as  now  constructed,  or 
in  other  heat  engines,  more  than  the  requisite  power  to  urge  a  system  of  rigid 
planes  through  the  air  at  a  great  velocity,  making  them  not  only  self-sustaining, 
but  capable  of  carrying  other  than  their  own  weight.  This  is  not  asserting 
that  they  can  be  steadily  and  securely  guided  through  the  air,  or  safely  brought 
to  the  ground  without  shock,  or  even  that  the  plane  itself  is  the  best  form 
of  surface  for  support ;  all  these  are  practical  considerations  of  quite  another 
order,  belonging  to  the  yet  inchoate  art  of  constructing  suitable  mechanisms 
for  guiding  heavy  bodies  through  the  air  on  the  principles  indicated,  and 
which  art  (to  refer  to  it  by  some  title  distinct  from  any  associated  with  bal- 
looning) I  will  provisionally  call  aerodromics*  With  respect  to  this  inchoate 
art,  I  desire  to  be  understood  as  not  here  offering  any  direct  evidence,  or 


*From  Htpoipotiiw,  to  traverse  the  air;  aspuSpoito'i,  an  air-runner. 


6  EXPERIMENTS    IN    AERODYNAMICS. 

expressing  any  opinion  other  than  may  be  implied  in  the  very  description  of 
these  experiments  themselves. 

It  is  just  to  say,  finally,  in  regard  to  the  extreme  length  of  time  (four  years) 
which  these  experiments  may  appear  to  have  taken,  that,  beyond  the  fact  of  their 
being  in  an  entirely  new  field,  nearly  all  imply  a  great  amount  of  previous  trial 
and  failure,  which  has  not  been  obtruded  on  the  reader,  except  to  point  out 
sources  of  wasted  effort  which  future  investigators  may  thus  be  spared,  and  that 
they  have  been  made  in  the  intervals  of  quite  other  occupations,  connected  with 
administrative  duties  in  another  city. 


CHAPTER  II. 

CHARACTER  AND  METHOD  OF  EXPERIMENTS. 

The  experiments  which  I  have  devised  and  here  describe,  are  made  with  one 
specific  object,  namely,  to  elucidate  the  dynamic  principles  lying  at  the  basis  of 
the  aerial  mechanical  flight  of  bodies  denser  than  the  air  in  which  they  move,  and 
I  have  refrained  as  a  rule  from  all  collateral  investigations,  hrwever  important, 
not  contributing  to  this  end.  These  experiments,  then,  are  in  no  way  concerned 
with  ordinary  aeronautics,  or  the  use  of  balloons,  or  objects  lighter  than  the  air, 
but  solely  with  the  mechanical  sustentation  of  bodies  denser  than  the  air,  and  the 
reader  will  please  note  that  only  the  latter  are  referred  to  throughout  this 
memoir  when  such  expressions  as  "planes,"  "models,"  "mechanical  flight," 
and  the  like,  are  used. 

The  experiments  in  question,  for  obtaining  first  approximations  to  the  power 
and  velocities  needed  to  sustain  in  the  air  such  heavy  inclined  planes  or  other 
models  in  rapid  movement,  have  been  principally  made  with  a  very  large 
whirling  table,  located  on  the  grounds  of  the  Allegheny  Observatory.  Allegheny, 
Pa.  (lat.  40°  27'  41.6" ;  long.  oh  20m  2.93s ;  height  above  the  sea-level,  1,145  feet). 

The  site  is  a  hill  on  the  north  of  the  valley  of  the  Ohio  and  rising  about  400 
feet  above  it.  At  the  time  of  these  observations  the  hill-top  was  bare  of  trees 
and  of  buildings,  except  those  of  the  observatory  itself.  This  hill-top  is  a  plane 
of  about  three  acres,  of  which  the  observatory  occupies  the  south  side.  The 
ground  slopes  rapidly  both  toward  the  east  and  west,  the  latter  being  the  quarter 
from  which  come  the  prevailing  winds. 

The  general  disposition  of  the  grounds  of  the  observatory  buildings,  of  the 
engine,  and  of  the  whirling  table  is  shown  in  plate  I.  The  whirling  table  is 
shown  in  plate  II,  in  elevation  and  in  plan,  and  with  details  on  an  enlarged  scale. 
It  has  been  constructed  especially  in  view  of  the  need  of  getting  the  greatest 
continuous  speed  thus  attainable,  under  circumstances  which  should  render 
corrections  for  the  effects  of  circular  motion  negligible,  in  relation  to  the  degree 
of  accuracy  aimed  at. 

The  first  disturbing  effect  of  circular  motion  to  present  itself  to  the  mind  of 
the  reader  will  probably  be  centrifugal  force;  but  in  regard  to  this  he  may  observe 
that  in  all  the  pieces  of  apparatus  hereafter  to  be  described,  the  various  parts  are 
so  disposed  that  the  centrifugal  force  proper,  viz.,  the  outward  thrust  of  the  plane 

(7) 


8  EXPERIMENTS    IN    AERODYNAMICS. 

or  model  which  is  the  subject  of  experiment,  shall  not  disturb  or  vitiate  the 
quantitative  data  which  are  sought  to  be  obtained. 

On  the  other  hand,  the  effects  of  circular  motion,  as  regards  the  behavior  of 
the  air  in  its  enforced  circulation,  are  only  to  be  obtained,  as  I  believe,  empir- 
ically, and  by  very  elaborate  experiments;  the  formulae  that  are  likely  to 
present  themselves  to  the  reader's  mind  for  this  computation,  largely  involving 
the  very  errors  of  fact  which  the  experiments  here  described  are  meant  to 
correct.  This  class  of  corrections  is,  then,  only  approximately  calculable,  and 
we  have  to  diminish  their  importance  by  the  use  of  so  large  a  circle  that  the 
motion  can  be  treated  as  (for  our  purpose)  linear.  To  show  that  these  corrections 
are  negligible  in  relation  to  such  degree  of  accuracy  as  we  seek,  we  may  advan- 
tageously consider  such  a  numerical  example  as  will  present  the  maximum  error 
of  this  sort  that  obtains  under  the  most  unfavorable  circumstances. 

Let  this  example  be  the  use  of  a  plane  of  the  greatest  length  hereafter 
described  in  these  experiments,  viz.,  30  inches,  and  let  us  suppose  its  center  to  be 
at  the  end  of  a  revolving  arm  30  feet  in  length,  which  was  that  employed. 

Let  us  suppose  the  plane  to  be  so  disposed  as  to  cause  the  effect  of  the 
inequality  of  air  resistance  arising  from  the  circular  motion  to  be  a  maximum, 
which  will  presumably  be  the  case  if  it  is  placed  parallel  to  the  arm  of  the  whirling 
table,  so  that  there  is  also  presumably  the  greatest  possible  difference  between  the 
pressure  on  the  outer  and  the  inner  half.  Under  these  circumstances  it  is  assumed 
in  the  experiments  detailed  in  the  following  chapters,  that  the  whole  plane  may 
be  treated  as  moving  with  the  linear  velocity  of  its  center,  and  it  will  be  now 
shown  that  this  assumption  is  permissible.  The  portions  of  the  plane  as  we  pro- 
ceed outward  from  the  center,  are  exposed,  on  the  whole,  to  a  greater  pressure, 
and  as  we  proceed  inward  to  the  center  to  a  less.  Using,  in  the  absence  of 
any  wholly  satisfactory  assumption,  the  well-known  one  implicitly  given  by  New- 
ton in  the  Principia,  that  the  pressure  of  the  air  at  every  point  of  the  plane  is 
strictly  proportional  to  the  square  of  the  velocity  with  which  it  is  moving  (thereby 
neglecting  the  secondary  effect  of  the  mutual  action  of  the  stream  lines  on  each 
other),  the  pressure  at  the  inner  end  of  the  plane  is  proportional  to  (281)-  — 826.6  ; 
at  the  outer  end  to  (314)*  =  976.6,  and  at  the  center  to  (30)-  =  900.  The  mean  of 
these  pressures  at  the  inner  and  outer  ends,  viz.,  901.6,  differs  from  the  pressure 
at  the  center  by  1.6,  or  less  than  one-fifth  of  one  per  cent ,  and  a  fortiori  the  inte- 
grated pressure  over  the  whole  area  in  this  and  still  smaller  planes,  differs  from 
the  pressure  computed  with  the  velocity  at  the  center,  by  less  than  the  same  amount. 
The  example  will,  it  is  hoped,  make  it  sufficiently  clear  that  such  disturbing 
effects  of  air-pressure  arising  from  circular  motion,  are  for  our  purposes  negligible, 
and  the  precautions  taken  against  other  detrimental  effects,  will  be  evident  from  a 
consideration  of  the  disposition  of  the  apparatus  employed  in  each  case. 


CHARACTER  AND  METHOD  OF  EXPERIMENTS.  9 

Most  of  the  various  experiments  which  I  have  executed  involve  measure- 
ments of  the  pressure  of  air  on  moving  planes,*  and  the  quantitative  pressures 
obtaining  in  all  of  these  experiments  are  of  such  magnitude  that  the  friction  of 
the  air  is  inappreciable  in  comparison.  This  fact  may  be  stated  as  the  result, 
both  of  my  own  experiments  (which  arc  here  only  indirectly  presented)  and  of 
well-known  experiments  of  others.f  It  will  be  seen  that  my  experiments  implicitly 
show  that  the  effect  of  friction  on  the  surfaces  and  at  the  speeds  considered  is  negli- 
gible, and  that  in  them  I  have  treated  the  actual  air-pressure  as  being  for  practical 
purposes  normal  to  the  surface,  as  in  the  case  of  an  ideal  fluid. 

The  whirling  table  consists  essentially  of  two  symmetrical  wooden  arms,  each 
30  feet  (9.15  meters)  long,  revolving  in  a  plane  eight  feet  above  the  ground.  Each 
arm  is  formed  of  two  continuous  parallel  strips  united  by  struts  as  shown  in  the 
plate,  and  is  made  at  once  broad  and  thin,  so  as  to  possess  the  requisite  lateral 
strength,  while  opposing  as  little  resistance  to  the  air  as  possible,  its  vertical 
rigidity  being  increased  by  guys.  The  arms  are  accordingly  supported  by  iron 
wires  extending  from  a  point  in  the  axis  about  8  feet  (2.5  meters)  above  the  table. 
An  enlarged  section  of  the  lower  end  of  the  axis  is  given  in  the  plate,  showing  the 
lower  bearing  and  the  position  of  the  bevel-wheels  connected  with  the  shaft,  which 
is  driven  by  the  engine.  A  lever  is  also  shown,  by  means  of  which  the  table  may 
be  lifted  out  of  its  gearing  and  revolved  by  hand.  The  gearing  is  so  disposed 
that  the  direction  of  rotation  is  always  positive — i.  e.,  clockwise  to  one  looking 
down  on  it.  The  whirling  table  was  driven  first  by  a  gas-engine  of  about  li  horse- 
power, but  it  was  found  inadequate  to  do  the  work  required,  and,  after  October 
20,  1888,  a  steam-engine  giving  10  horse-posver  was  used  in  its  stead.  This 
was  a  portable  engine  of  10-inch  stroke,  having  a  fly-wheel  giving  from  60  to 
150  revolutions  per  minute,  but  ordinarily  run  at  about  120  revolutions,  with  90 
pounds  of  steam.  The  belt  of  either  engine  communicates  its  motion  to  a  set  of' 
step-pulleys,  by  means  of  which  four  different  velocity-ratios  can  be  obtained. 
These  pulleys  turn  a  horizontal  shaft  running  underground  to  the  axis  of  the 
turn-table,  as  indicated  on  the  ground  plan  of  the  engine-house  at  A,  and  also 

*  Since  it  is  impossible  to  construct  absolutely  plane  surfaces  at  once  very  thin  and  very  rigid,  those  "  planes  " 
in  actual  use  have  been  modified  as  hereafter  described.  They  have  all,  however,  it  will  be  observed,  square  and 
not  rounded  edges,  and  it  should  be  likewise  observed  that  the  values  thus  obtained,  while  more  exactly 
calculable,  give  less  favorable  results  than  if  the  edges  were  rounded,  or  than  if  the  section  of  the  plane  were 
such  as  to  give  "  stream  lines." 

t  There  is  now,  I  believe,  substantial  agreement  in  the  view  that  ordinarily  there  is  no  slipping  of  a  fluid 
past  the  surface  of  a  solid,  but  that  a  film  of  air  adheres  to  the  surface,  and  that  the  friction  experienced  is 
largely  the  internal  friction  of  the  fluid — i.  e.,  the  viscosity.  Perhaps  the  best  formula  embodying  the  latter  is 
given  by  Clerk  Maxwell  in  his  investigation  on  the  coefficient  of  the  viscosity  of  the  air.  This  is  /j.  =  0.0001878 
(1  •+  .0027  V),  //  and  (I  being  taken  as  defined  in  his  paper  on  the  dynamical  theory  of  gases  in  Phil.  Trans.,  Vol. 
CLVII.  By  this  formula  the  actual  tangential  force  on  a  one-foot-square  plane  moving  parallel  to  itself  through 
the  air  at  the  rate  of  100  feet  a  second  is  1,095  dynes  (0.08  poundals),  or  less  than  -V  of  1  per  cent,  of  the  pressure 
on  the  same  plane  moving  normally  at  this  speed,  and  hence  theory  as  well  as  ob.survation  shows  its  negligibility. 
2 


10  EXPERIMENTS    IN    AERODYNAMICS. 

on  the  elevation  at  A',  where  it  is  shown  as  geared  to  this  vertical  axis  by  a  pair 
of  bevel-wheels,  that  of  the  shaft  having  15  teeth  and  that  of  the  turn-table  axis 
having  75  teeth,  or  1  to  5.  The  cone-pulleys  used  from  the  beginning  of  the 
experiments  up  to  September,  1890,  have  four  steps  with  diameters  of  21i,  18i, 
116,  and  8  inches.  The  speeds  given  by  these  pulleys  in  terms  of  whirling-table 
revolutions  for  1,000  revolutions  of  the  gas-engine  are  approximately — 

Lowest  speed 25 

Second     "      50 

Third       "      100 

Highest    "      200 

The  gas-engine  speed  varied  from  180  to  190  revolutions  per  minute. 

In  September,  1890,  the  above-described  pulleys  were  replaced  by  a  larger 
set  of  three  steps,  having  diameters  of  36,  25i  and  18  inches,  respectively,  which 
give  speeds  in  the  ratio  of  4,  2,  and  1,  and  the  gear,  which  had  broken,  was 
replaced  by  a  new  one  of  1  to  4. 

This  system  gives  for  120  revolutions  of  the  steam-engine  per  minute, 
driving — 

18    in.  pulley,  48  revolutions  of  turn-table  per  minute  =  100  +  miles  per  hour  at  end  of  arm. 

25J  "        "       24  "  "  "  =50   +     "  " 

36    "        "       12  "  "  "  =25    +     "  "  "          " 

By  regulating  the  speed  of  the  engine  any  intermediate  velocities  can  be 
obtained,  and  thus  the  equipment  should  be  susceptible  of  furnishing  speeds 
from  10  to  100  miles  per  hour  (4.5  to  45  meters  per  second) ;  but  owing  to  the 
slipping  of  belts  the  number  of  turn-table  revolutions  was  less  than  this  for 
the  higher  velocities,  so  that  the  highest  attained  in  the  experiments  did  not 
reach  this  upper  limit,  but  was  a  little  over  100  feet  (30  meters)  per  second,  or 
about  seventy  miles  per  hour.  The  precise  velocity  actually  attained  by  the 
turn-table  is  determined,  quite  independently  of  the  speed  of  the  engine,  by  an 
electrical  registration  on  the  standard  chronograph  in  the  observatory.  The 
electrical  current  passes  into  four  fixed  contact-pieces  (shown  at  0-P,  plate  II, 
and  on  large  scale  in  plate  III)  fastened  to  a  fixed  block  placed  around  the 
axis  of  the  whirling  table,  these  fixed  pieces  being  placed  symmetrically  around 
the  axis,  while  another  platinum  contact-piece  is  fastened  to  a  horizontal  arm 
screwed  into  the  axis  of  the  turn-table  and  revolving  with  it,  thus  "  making 
circuit  "  every  quarter  revolution  of  the  table.  The  current  passes  out  of  the  axis 
through  a  brush  contact,  shown  in  plate  III,  and  thence  to  the  chronograph  in  the 
observatory.  C  designates  the  fixed  contact  pieces,  and  P  the  platinum  piece 
revolving  with  the  axis.  S  and  L  are  adjusting  screws.  Turning  again  to  plate 
II,  an  additional  brush  contact,  shown  at  B,  and  again  at  B',  serves  to  transmit 


CHARACTER  AND  METHOD  OF  EXPERIMENTS.  11 

a  current  to  wires  running  out  to  the  end  of  the  whirling  arm,  so  that  seconds 
from  the  mean  time  clock  and  other  phenomena  can  be  registered  on  the  recording 
cylinder  of  the  dynamometer  chronograph  at  the  end  of  the  arm;  and  also 
phenomena  taking  place  at  the  end  of  the  arm  can  be  registered  on  the  chrono- 
graph in  the  observatory.  By  these  means  the  experiments  are  put  under 
electric  control  and  perfect  knowledge  is  obtained  of  the  velocity  of  the  turn- 
table at  the  moment  when  any  phenomenon  occurs.  This  brush  contact  was 
made  sufficiently  large  and  heavy  to  transmit  a  current  from  a  dynamo  to  an 
electric  motor  placed  on  the  whirling  arm,  and,  having  this  electric  equipment 
extending  to  the  outer  end  of  the  whirling  arm,  different  pieces  of  apparatus 
were  devised  for  registering  pressure  and  other  phenomena  there. 

The  whirling  table  was  thus  established  and  the  experiments  conducted  in 
the  open  air,  not  through  choice,  but  because  the  erection  of  a  large  building 
specially  designed  for  them  was  too  expensive  to  be  practicable.  It  was  hoped 
to  take  advantage  of  calm  days  for  the  performance  of  experiments,  as  in  a  calm, 
a  whirling  table  in  the  open  air  is  under  the  best  possible  conditions,  for  in  a 
confined  building  the  rotating  arm  itself  sets  all  the  air  of  the  room  into  slow 
movement,  besides  creating  eddies  which  do  not  promptly  dissipate.  Practically, 
however,  these  calm  days  almost  never  came,  and  the  presence  of  wind  currents 
continued  from  the  beginning  to  the  end  of  the  experiments,  to  be  a  source  of 
delay  beyond  all  anticipation,  as  well  as  of  frequent  failure. 

In  the  latter  part  of  April,  1889,  an  octagon  fence  20  feet  high  (shown  on 
plate  I)  was  erected  around  the  whirling  table  with  the  object  of  cutting  off,  to 
some  extent,  the  access  of  the  wind.  This,  however,  proved  to  be  ineffectual,  and 
the  difficulty  experienced  from  the  wind  continued  nearly  unabated. 

If  any  one  should  propose  to  repeat  or  extend  these  experiments,  I  would 
advise  him,  first  of  all,  and  at  all  costs,  to  establish  his  whirling  table  in  a  large, 
completely  inclosed  building. 


CHAPTER  III. 

THE  SUSPENDED  PLANE. 

The  first  instrument,  called  the  Suspended  Plane,  was  devised  to  illustrate 
an  unfamiliar  application  of  a  known  principle.  I  call  the  application  ''un- 
familiar" because  distinguished  physicists  have  held,  for  instance,  that  a  bird 
(which  obviously  expends  a  certain  amount  of  muscular  effort  in  simply  hovering 
in  the  air)  must  expend  in  flight  all  the  effort  required  for  hovering,  together 
with  so  much  additional  energy  as  is  required  to  overcome  the  resistance  of 
the  air  to  its  horizontal  motion,  so  that  the  energy  expended  increases  with  the 
velocity  attained,*  while  the  consideration  of  the  action  of  the  suspended  plane 
indicates,  if  it  do  not  demonstrate,  that  the  opposite  view  is  the  true  one,  and 
thus  serves  as  a  useful  introduction  to  the  demonstrative  experiments  I  have 
spoken  of  as  coming  later. 

*This  view  of  flight  received  indorsement  from  a  source  of  the  highest  authority  in  a  report  by  Gay-Loaeac, 
l-'lourens,  and  Navier,  accepted  and  published  by  the  Institute  of  France  in  1830.  [Navier,  C.  L.  M.  II. — Rapport 
sur  un  Memoire  de  M.  Chabrier  concernant  les  moyens  de  voyager  dans  1'air  et  de  s'y  diriger,  contcnont  une 
nouvelle  theorie  des  mouvemenU  progressifs.  (Commissaires,  MM.  Gay-Lussac,  Flourens,  et  Navier,  rapporteur.) 
Paris,  Mem.  Acad.  Sci.  xi,  1832  (Hist.),  pp.  61-118.]  The  report  is  drawn  up  by  Navier,  to  whom  the  mathe- 
matical investigation  is  due.  He  formulates  the  differential  equations  of  motion  for  the  two  cases  of  hovering 
and  horizontal  flight,  integrates  them  in  the  customary  way,  assumes  approximate  values  for  the  constants  of 
the  equations,  and  computes  the  work  expended  by  an  ordinary  swallow  with  the  following  results:  For 
hovering,  the  work  done  per  second  by  the  swallow  is  approximately  equal  to  the  work  required  to  raise  its  own 
weight  eight  meters.  While  in  horizontal  flight  the  work  done  varies  as  the  cube  of  the  velocity,  and  for  15 
meters  per  second  is  equal  to  5.95  kilogramineters  per  second,  or  enough  to  raise  its  weight  390  meters.  Thiy 
isjifty  times  as-much  as  that  expended  in  hovering,  or  in  English  measures,  over  2,500  foot-pounds  per  minute, 
which  is  a  rate  of  working  greater  than  a  man  has  when  lifting  earth  with  a  spade. 

The  same  computation  applies  to  any  larger  bird  whose  weight  bears  the  same  ratio  to  the  extent  of  its 
wings.  In  view  of  these  figures  Navier  suggests  that  there  exists  the  same  ratio  between  tlic  efforts  necesssary  for  sim/ili- 
suspension  and  for  rapid  fight  as  exists  for  terrestrial  animals  between  the  effort  required  for  standing  upright  and  that 
required  for  running.  [Nous  remarquerons  la  grande  difference  qui  existe  entre  la  force  necessaire  pour  que  1'oiseau 
se  soutienne  simplement  dans  1'air,  et  celle  qu'exige  un  mouvement  rapide.  Lorsque  la  vitesse  de  ce  mouvement 
est  de  15°  par  seconde,  on  trouve  que  cette  derniere  force  est  environ  cinquaiiie  fois  plus  grande  que  la  premiere. 
Ainsi  1'effort  qu'exerce  1'oiseau  pour  se  soutenir  dans  1'air  est  fort  petit  comparativement  a  1'effort  qu'il  exe'rce 
dans  le  vol.  II  en  coute  peut-etre  moins  de  fatigue  a  1'oiseau  pour  se  soutenir  simplement  dans  1'air,  eu  egard  a 
la  fatigue  qu'il  est  capable  de  supporter,  qu'il  ne'en  coilte  a  1'homme  et  aux  quadruples  pour  se  soutenir  debout 
sur  leurs  jambes." — Paris,  Mem.  Acad.  Sci.  xi,  1832  (Hist.),  p.  71.]  The  supposed  elegance  and  validity  of 
Navier's  mathematical  processes,  and  especially  the  elaboration  with  which  they  were  carried  out,  appears  to 
Iiave  obscured  the  absolutely  inadmissible  character  of  these  results,  and  they  received  the  unqualified  adherence 
of  the  remainder  of  the  committee.  This  report  thereupon  became  a  standard  authority  upon  the  theory  of 
•(light,  and  continued  to  be  so  accepted  for  many  years. 

(12) 


THE   SUSPENDED   PLANE.  13 

The  suspended  plane  (plate  IV)  consists  of  a  thin  brass  plane  one  foot  square, 
weighing  two  pounds,  hung  vertically  by  a  spring  from  a  surrounding  frame. 
Eight  delicate  friction  rollers  AA',  BB'  enable  the  plane  to  move  freely  along 
the  frame,  but  prevent  any  twisting  or  lateral  motion,  the  use  of  the  guide-frame 
being  to  prevent  the  plane  from  so  "  flouncing  "  under  irregular  air  currents  that 
its  pull  cannot  be  measured.  The  guide-frame  carrying  the  plane  turns  symmet- 
rically about  an  axis,  CC',  so  that  the  gravity-moment  about  the  axis  is  simply 
the  weight  of  the  plane  on  a  lever  arm  measured  from  its  center.  The  axis 
CC'  rests  upon  a  standard  which  is  placed  upon  the  whirling  arm.  A  pencil,  P, 
attached  to  the  plane  is  pressed  by  a  spring  against  a  registering  card  at  the  side 
of  the  plane  and  perpendicular  to  it.  The  card  contains  a  graduated  arc  whose 
center  is  at  C  and  whose  zero  angle  is  under  the  pencil  point  at  the  vertical 
position  of  the  plane.  The  distance  of  the  trace  from  the  center  C  registers 
the  extension  of  the  spring. 

When  the  plane  is  at  rest  the  extension  of  the  spring  measures  the  weight 
of  the  plane.  When  the  plane  is  driven  forward  horizontally  the  pressure  of 
the  wind  on  the  plane  inclines  it  to  an  angle  with  the  vertical,  and  the  higher 
the  speed  the  more  it  is  inclined.  For  any  position  of  equilibrium  there  is 
neither  upward  nor  downward  pressure  on  the  guide-frame,  and  the  whole 
resulting  force  acting  on  the  plane,  both  that  of  gravity  and  that  arising  from  the 
wind  of  advance,  is  borne  by  the  spring. 

The  apparatus  being  mounted  at  the  end  of  the  arm  of  the  large  whirling 
table  and  being  still,  the  weight  of  the  plane  is  registered  by  an  extension  of 
the  suspending  spring  corresponding  to  two  pounds.  Next,  lateral  motion  being 
given  (from  the  whirling  table)  and  the  plane  being  not  only  suspended  but 
dragged  forward,  the  spring  is  seen  not  to  be  extended  further,  but  to  contract, 
and  to  contract  the  more  as  the  speed  increases.  The  drawing  contains  a  copy 
of  the  trace  made  by  the  pencil  upon  the  recording  sheet,  showing  how  the 
spring  contracts  with  the  increasing  angles  of  the  plane  with  the  vertical,  where 
these  angles  correspond  to  increasing  velocities  of  translation,  or,  we  may  almost 
say,  to  increasing  speeds  of  flight.  The  experiment  also  calls  attention  to  the 
fundamental  circumstance  that  in  the  horizontal  flight  of  an  aeroplane  increasing 
speeds  are  necessarily  accompanied  by  diminishing  angles  of  the  plane  with  the 
horizontal. 

The  experiment  may  perhaps  be  held  to  be  superfluous,  since  the  principle 
involved,  that  the  pressure  of  a  fluid  is  always  normal  to  a  surface  moving  in  it, 
is  already  well  known  ;  but  we  must  distinguish  between  the  principle  and  its 
application.  Though  when  attention  is  called  to  it,  the  latter  is  seen  to  be  so 
immediate  a  consequence  of  the  principle  as  to  appear  almost  self-evident,  I  must 
still  call  the  application  "unfamiliar"  since,  as  will  be  seen,  it  indicates  the  way 


14  EXPERIMENTS    IN    AERODYNAMICS. 

to  consequences  which  may  appear  almost  paradoxical,  such  as  that  in  horizontal 
frictionless  flight,  the  greater  the  speed,  the  less  the  power  required  to  maintain  it. 
I  do  not  mean  that  this  illustration  as  here  given,  offers  a  satisfactory  demonstration 
of  this  last  consequence,  but  that  any  one  who  has  really  always  possessed  the 
idea  that  the  experiment  suggests,  in  its  full  import,  must  have  been  inclined  to 
admit  the  possibility  that  machine  flight  grows  more  and  more  economical  of 
power  as  higher  speeds  are  attained — and  this  is  not  self-evident. 

This  preliminary  apparatus  can  indeed,  with  little  modification,  be  used  to 
demonstrate  this  fact,  but  it  is  actually  presented  here,  it  will  be  noticed,  not  as 
demonstrative,  but  as  illustrative,  of  the  possibility  suggested  ;  a  possibility  whose 
fundamental  importance  justifies,  and  indeed  demands,  the  fullest  demonstration, 
which  can  be  better  supplied  by  apparatus  designed  to  give  data  of  precision  for 
computing  the  actual  work  done  in  flight  at  different  speeds ;  data  which  will  be 
furnished  here  subsequently  from  quite  other  experiments. 


CHAPTER  IV. 

THE  RESULTANT  PRESSURE  RECORDER. 

As  preliminary  to  obtaining  the  data  mentioned  at  tlie  close  of  the  last 
chapter,  it  is  desirable  to  determine  experimentally  the  direction  of  pressure  of 
the  air,  (since  the  air  is  not  an  ideal  fluid  such  as  the  theory  contemplates,)  on  an 
inclined  plane,  and  to  investigate  the  assumption  made  by  Newton  that  the 
pressure  on  the  plane  varies  as  the  square  of  the  sine  of  its  inclination. 

The  second  instrument  constructed  was,  then,  for  the  purpose  of  obtaining 
graphically,  the  direction  of  the  total  resultant  pressure  on  an  inclined  plane 
(in  practice  a  square  plane)  and  roughly  measuring  its  amount.*  For  this  reason 
it  will  be  called  here  the  Resultant  Pressure  Recorder. 

DESCRIPTION. 

Plate  V  contains  drawings  of  the  instrument.  Upon  a  base-board,  BB',  is  a 
standard,  E,  carrying  an  arm,  AA',  hung  symmetrically  in  gimbal  joints.  On 
the  outer  end  of  the  arm  a  one-foot-square  plane  (called  here  the  wind  plane)  is 
fastened  with  a  clamp,  and  a  graduated  circle  assists  in  setting  the  plane  at 
different  angles  of  inclination  to  the  horizon.  The  extremity  of  the  inner  end  of 
the  arm  carries  a  pencil,  P,  which  registers  on  the  surface  of  a  vertical  plane,  which 
is  in  practice  a  sheet  of  diagram  paper  clamped  on  the  surface  FF'  of  an  upright 
circular  board  fixed  by  a  standard  to  the  base-board  BB'.  The  pencil-holder  H 
fits  closely  into  a  ring  at  the  center  of  a  system  of  four  equal  radial  springs  attached 
to  a  circular  frame,  MM',  projecting  immediately  in  front  of  the  registering 
board  and  concentric  with  it.  This  frame  MM'  is  connected  by  supports  to  a 
close-fitting  ring,  which  closes  around  the  registering  board  and  serves  as  a  holder 
for  the  diagram  sheets  which  are,  as  stated,  clamped  on  the  face  FF'  of  the  cir- 
cular board.  The  radial-spring  system  and  its  frame  may  be  rotated  about  the 
registering  board,  so  that  the  diagram  sheet  may  be  rotated  in  its  own  plane. 
The  inner  or  recording  end  of  the  arm  is  weighted  so  as  exactly  to  counterpoise 
the  outer  end  carrying  the  wind  plane.  Hence  this  plane  is  virtually  weightless, 

*  Observations  of  the  pressure  on  inclined  planes  have  been  made  by  previous  experimenters,  the  first  being 
by  Button  in  the  summer  of  1738,  just  100  years  before  those  about  to  be  recorded.  But  in  the  experiments  of 
Hutton,  aa  well  as  in  most  of  the  later  ones,  the  horizontal  component  of  the  pressure  on  the  inclined  plane  has 
been  the  subject  of  measurement,  while  the  apparatus  about  to  be  described  affords  a  measurement  of  the  total 

normal  pressure  on  the  plane. 

(15) 


16  EXPERIMENTS    IN    AERODYNAMICS. 

and  when  the  apparatus  is  at  rest  the  pencil-point  rests  in  the  center  of  the 
radial  springs  without  pressure  upon  them,  but  when  any  force  changes  this 
position  of  equilibrium  it  is  resisted  and  measured  by  the  resultant  extension  of 
the  four  radial  springs,  shown  by  a  definite  departure  of  the  pencil  from  the 
center  in  a  definite  direction. 

The  tension  of  these  springs  is  determined  before  the  apparatus  is  mounted 
for  trial,  by  rotating  the  frame  MM'  about  a  longitudinal  (imaginary)  axis  passing 
through  the  centers  of  the  wind  plane  and  registry  plane.  If  the  pencil  end  of 
the  arm  be  weighted  with  (for  instance)  one  pound,  it  traces  out  a  curve  on  the 
paper  corresponding  to  a  one-pound  tension  in  every  direction.  With  two  pounds 
another  and  larger  curve  is  described,  and  so  on  till  the  resultant  pressure  of  the 
four  radial  springs  are  then  tabulated  for  every  direction  and  every  pressure 
which  the  wind  of  advance  may  later  be  expected  to  exercise.  These  curves  are 
in  practice  very  nearly  circles. 

The  distance  from  the  pencil  to  the  gimbals  is  the  same  as  that  from  the 
gimbals  to  the  center  of  the  wind  plane,  so  that  the  wind  pressure,  considered  as 
acting  at  the  center  of  the  plane,  has  the  same  lever  arm  as  the  pressure 
imposed  by  the  extended  springs.  It  should  be  particularly  noted  as  a  con- 
sequence of  the  above-described  conditions  that,  although  the  wind  plane  is 
perfectly  free  to  move  in  every  direction,  it  is  not  free  to  rotate — i.  e.,  it  is 
always  during  this  motion  parallel  to  itself. 

The  only  other  feature  of  the  construction  to  be  noted  is  the  combination  of  a 
spring  and  an  electro-magnet  connected  with  the  recording  pencil.  The  pencil  is 
held  away  from  the  paper  by  means  of  the  spring  until  a  desired  velocity 
of  rotation  of  the  turn-table  is  attained,  when  by  means  of  the  electro-magnet  the 
pencil  is  released  and  allowed  to  record. 

The  method  of  using  the  apparatus  is  as  follows  :  The  wind  plane  is  set  at 
an  angle  of  elevation  a  ;  a  disk  of  paper  is  placed  upon  the  recording  board  and 
oriented  so  that  a  line  drawn  through  its  center  to  serve  as  a  reference  line  is 
exactly  vertical.  The  whirling  table  is  then  set  in  motion,  and  when  a  uniform 
velocity  has  been  attained  a  current  is  passed  through  the  electro-magnet  and 
the  pencil  records  its  position  on  the  registering  sheet.  Since  gravity  is  virtually 
inoperative  on  the  counterpoised  plane,  the  position  of  this  trace  is  affected  by 
wind  pressure  alone  and  is  experimentally  shown  to  be  diametrically  opposite  to 
its  direction,  while  the  radial  distance  of  the  trace  from  the  center  is  evidently  a 
measure  of  the  pressure  on  the  plane.  Thus  the  instrument  shows  at  the  same 
time  the  direction  and  magnitude  of  the  resultant  wind  pressure  on  the  plane  for 
each  inclination  of  the  plane  and  for  different  velocities  of  the  whirling  table. 
Since  the  arms  of  the  apparatus  are  exposed  to  the  wind  of  rotation,  the  outer 
end,  moving  with  greater  velocity  than  the  inner  end,  will  be  subject  to  a  slightly 


THE    RESULTANT    PRESSURE    RECORDER. 


17 


greater  pressure.  Preliminary  experiments  were  therefore  made  without  the  wind 
plane  for  detecting  this  effect,  with  the  result  that  no  sensible  difference  was 
apparent  between  the  pressure  on  the  inner  and  outer  arm,  even  at  the  highest 
speeds. 

On  August  25,  1888,  the  spiral  springs  were  calibrated  by  hanging  weights 
of  1,  2,  and  3  pounds  to  the  center  of  the  springs  and  marking  the  displaced 
position  of  the  center  when  the  system  was  rotated  through  successive  octants  in 
the  manner  already  described.  Experimental  circles  were  drawn  through  the 
system  of  points,  and,  the  departures  of  the  individual  points  being  very  small, 
the  circles  were  adopted  as  the  curves  giving  the  relation  between  pencil  excursions 
and  pressures.  From  these  curves  the  following  table  has  been  constructed : 

TABLE  I. 


Excursion  of  trace. 

Pressure. 

Excursion  of  trace. 

Pressure. 

Centimeters. 

Lbs. 

Grammes. 

Centimeters. 

Lbs. 

Grammes. 

0.28 

0.1 

45 

4.45 

1.6 

726 

0.55 

0.2 

91 

4.73 

1.7 

771 

0.82 

0.3 

136 

5.03 

1.8 

816 

1.10 

0.4 

181 

5.33 

1.9 

862' 

1.37 

0.5 

227 

5.65 

2.0 

907 

1.64 

0.6 

272 

5.98 

2.1 

953 

1.92 

0.7 

318 

6.29 

2.2 

998 

2.20 

0.8 

363 

6.60 

2.3 

1043 

2.47 

0.9 

408 

6.91 

2.4 

1089 

2.73 

1.0 

454 

7.25 

2.5 

1134 

3.02 

1.1 

499 

7.60 

2.6 

1179 

3.30 

1.2 

545 

7.93 

2.7 

1225 

3.59 

1.3 

590 

8.28 

2.8 

1270 

3.89 

1.4 

635 

8.63 

2.9 

1315 

4.17 

1.5 

680 

9.00 

3.0 

1361 

After  many  days  of  preliminary  experimentation,  in  which  the  instrument 
was  gradually  perfected  by  trial  in  successive  forms  before  being  brought  to  the 
condition  to  which  the  foregoing  description  applies,  two  days'  experiments  were 
made  on  August  27  and  28,  and  a  final  series  on  October  4,  1888.  These 
are  presented  in  detail  in  the  accompanying  tables,  and  consist  of  sixty-four 
separate  experiments  made  with  the  plane  set  vertical  and  at  angles  varying 
between  5°  and  45°  with  the  horizon.  The  mean  temperature  is  obtained  from 
thermometer  readings  at  the  beginning  and  end  of  each  set  of  experiments,  which 
usually  continued  from  one  to  two  hours.  The  mean  wind  velocity  is  obtained 
from  the  readings  of  a  Casella  air  meter.  The  apparatus  is  so  placed  upon  the 
whirling  arm  that  the  center  of  the  wind  plane  is  nine  meters  from  the  axis  of 
rotation.  One  registering  sheet  serves  for  a  group  of  observations,  consisting  in 

3 


18  EXPERIMENTS    IN    AERODYNAMICS. 

general  of  a  succession  of  settings  of  the  wind  plane  beginning  with  a  setting  at 
90°  and  followed  by  diminishing  angles  of  elevation.  At  each  setting  two  obser- 
vations are  usually  obtained  by  turning  the  register  sheet  through  an  angle  of 
180°.  Thus  the  two  traces  made  at  the  same  setting  should  lie  in  a  straight 
line  passing  through  the  center. 

The  method  adopted  in  reading  the  traces  is  as  follows :  Straight  lines  are 
drawn  through  the  center  and  the  two  traces  made  at  each  setting  of  the  plane. 
The  angle  is  then  measured  between  the  trace  of  the  plane  at  90°  and  the  traces 
corresponding  to  other  settings.  The  pressure  being  normal  to  the  plane,  these 
measured  values  should  be  the  complement  of  the  angles  of  elevation  at  which 
the  plane  is  set.  It  will  be  seen  by  inspection  of  the  accompanying  tables  that 
this  relation  approximately  obtains. 

Tables  II,  III,  and  IV  contain  all  the  original  data  of  the  experiments  and 
their  reduction.  The  first  columns  require  no  explanation.  The  fifth  column 
(Tables  II  and  III)  gives  the  angle  measured  on  the  register-sheet  between  the 
radial  direction  of  each  trace  and  the  direction  of  the  trace  made  when  the  plane 
was  set  vertical.  The  sixth  column  gives  the  measured  distance  of  the  trace  from 

the  center,  and  the  seventh  gives  the  results  of  these  extensions  converted  into 

p 

pressure  on  the  plane  by  means  of  Table  I.  The  column  headed  km  —  ^  contains 

't 

the  results  of  measurements  of  pressure  on  the  normal  plane  expressed  in  terms 
of  the  coefficient  km  of  the  equation  P  =  km  F2,  in  which  Fis  the  velocity  of  the 
plane  in  meters  per  second  and  P  the  pressure  on  the  plane  in  grammes  per  square 
centimeter,  the  subscript  m  being  used  to  designate  units  of  the  metric  system. 


THE    RESULTANT    PRESSURE    RECORDER. 


19 


Experiments  with  the  Resultant  Pressure  Recorder  to  determine  the  resultant  pressure,  on  a  square 
plane  moved  through  the  air  with  different  velocities  and  different  inclinations. 

TABLE  II.— AUGUST  27, 1888. 
S.  P.  LANGLEY,  Conducting  experiments;  F.  W.  VERY,  Assisting. 

Wind  plane,  1  foot  square  (929  square  centimeters) ;  center  of  wind  plane,  9  m.  from  axis  of 
rotation;  barometer,  736  mm. ;  temperature  at  6  p.  m.,  21°.0  C. ;  mean  wind  velocity, 0.52  meters 
per  second. 


Time  of  observation. 

<x> 

03 

"AC 
.   O 

11 
1j« 
*$ 

f 

•< 

Seconds  in  one  revo- 
lution of  turn-table. 

Linear  velocity  of  cen- 
ter of  wind  plane. 
F  (meters  per  sec.). 

Angle  of  trace  with  di- 
rection of  trace  made 
by  plane  set  at  90°. 

Departure  of  trace 
from  center  (centi- 
meters). 

Pressure  on  plane. 
Pa  (grammes  per 
sq.  centimeter). 

km= 

P 

V 

P»- 

.0077  V- 

Pa 

Pm 

(p.m.) 
5-45 

90° 

1265 

447 

1  10 

0195 

00097 

90 

12.64 

447 

1  05 

0185 

00092 

30 

12.58 

449 

57°  8 

100 

0176 

0156 

1  13 

15 

12.67 

4.46 

75  .8 

050 

0.088 

0153 

058 

6-06 

90 

653 

866 

280 

0495 

00066 

90 

6.60 

857 

280 

0495 

00067 

30 

6.55 

864 

54   5 

260 

0463 

0575 

080 

15 

6.44 

878 

73   5 

165 

0.293 

0594 

049 

75 

644 

878 

92   0 

080 

0141 

0594 

024 

7.5 

643 

879 

83   0 

080 

0141 

0595 

024 

6:29 

90 

5.74 

9.85 

410 

0722 

0.0075 

90 

539 

1050 

440 

0771 

00070 

30 

487 

1161 

60   3 

465 

0.820 

1038 

079 

EXPERIMENTS    IN    AERODYNAMICS. 


TABLE  III.— AUGUST  28, 1888. 
S.  P.  LANQLEY,  Conducting  experiments;  F.  W.  VERY,  Assisting. 

Wind  plane,  1  foot  square  (929  square  centimeters) ;  center  of  wind  plane,  9  m.  from  axis  of 
rotation ;  barometer,  736.6  mm. ;  temperature,  19°.4  C. ;  mean  wind  velocity,  0.37  meters  per 
second. 


Time,  of  observation. 

o> 

i 

Old 

T>8 

J-S 

g.g« 

o£ 

•S.I 
I 

Seconds  in  one  revo- 
lution of  turn-table. 

Linear  velocity  of  cen- 
ter of  wind  plane. 
V  (meters  per  sec.). 

Angle  of  trace  with  di- 
rection of  trace  made 
by  plane  set  at  90°. 

°.A 

J£j 
fl> 
0 

^     t-t 

°  3 

s§- 

s  °  2 
SS-S 

030° 

8*  a 

Q 

2  §3 

g  ft 

*lf 

8  1.1 

c3  %j 

l"§ 
l^'g* 

hm  

p 

V 

P»= 

.0077  V1 

P. 
5, 

(p.  m.) 
2-26 

90° 

12.62 

448 

103 

0180 

00090 

90 

1262 

448 

100 

0176 

00088 

30 

1262 

448 

65°  8 

070 

0122 

0155 

0.79 

15 

1257 

450 

78   8 

065 

0112 

0156 

0.72 

2-52 

90 

645 

877 

325 

0576 

00075 

90 

652 

867 

315 

0561 

00075 

45 

648 

873 

48   5 

330 

0585 

0587 

1.00 

45 

651 

869 

46  0 

310 

0551 

0581 

0.95 

30 

645 

877 

61   5 

300 

0532 

0592 

0.90 

30 

645 

877 

60  5 

320 

0566 

0592 

0.96 

15 

643 

879 

75   6 

205 

0366 

0595 

0.61 

15 

640 

884 

76  5 

1  90 

0341 

0602 

0.57 

75 

644 

878 

86  0 

145 

0259 

0594 

044 

75 

645 

877 

80  5 

1  15 

0205 

0592 

0.35 

3-40 

90 

505 

11.20 

5.40 

0.930 

0.0074 

90 

534 

10.59 

4.50 

0.786 

0.0070 

45 

519 

1090 

48   0 

400 

0702 

0915 

0.77 

45 

529 

1069 

48   0 

410 

0722 

0880 

0.82 

30 

526 

1075 

60  5 

440 

0771 

0.890 

0.87 

30 

544 

1040 

59   0 

390 

0683 

0833 

082 

15 

509 

11  11 

81   0 

235 

0415 

0950 

0.44 

15 

5  18 

1092 

75   5 

220 

0387 

0918 

0.42 

75 

495 

11  42 

84   5 

1  30 

0230 

1004 

0.23 

75 

533 

1061 

85   5 

145 

0259 

0867 

0.30 

4-30 

90 

579 

977 

390 

0.683 

0.0072 

90 

578 

978 

385 

0.673 

0.0070 

30 

553 

1023 

59  0 

385 

0673 

0806 

0.84 

30 

556 

1017 

58   8 

360 

0634 

0.796 

0.80 

75 

541 

1045 

85   0 

1  20 

0215 

0.841 

0.26 

75 

509 

11  11 

75   0 

175 

0312 

0.950 

0.33 

REMARKS. — During  these  experiments  the  slight  breeze  has  almost  died  away ;  angle  of  mean 
trace  made  by  plane  set  at  90°  with  vertical  plumb  line  drawn  on  register  sheet  =  95°. 


THE    RESULTANT    PRESSURE    RECORDER 


21 


TABLE  IV.— OCTOBER  4,  1888. 
F.  W.  VERY,  Conducting  experiments ;  JOSEPH  LUDEWIG,  Assisting. 

Wind  plane,  1  foot  square  (929  square  centimeters) ;  center  of  wind  plane,  9  m.  from  axis  of 
rotation;  barometer,  732.3  mm.;  temperature  10:15  a.  m.,  48°  F. ;  2:30  p.  m.,  56°  P.;  mean 
temperature,  52°  F.  =  ll°.l  C. ;  mean  wind  velocity,  0.85  meters  per  second. 

During  these  experiments  both  the  velocity  of  the  wind  and  its  direction  were  quite  variable. 


1 

a) 

II 

§  a^ 

o  cj  a> 

o  '^3 

S  "- 

§|  . 

1 

*I 

§3 

O  ft  ^ 

"**  o 
^—  ' 

it 

k  — 

§3 

_g-£ 

0  «S 

>^H    r< 

O    a) 

rt  S  * 

m 

P  _ 

n 

05 

~.  3 

O  .3  m 

-+J 

S  f5  S 

^90— 

Pm 

1 

(4-1 

0 
0> 

r2'"S 

3Z 

a.  ° 
T3  a 
aj 

1^1 

®  §^A 

8  °  E 

c3   o    <I> 

l^s 

p 

V 

.0076  V 

a 

a 

O    ^ 

d  *i  ^ 

§<efc!    8 

S  ^  « 

£ 

CB'" 

^ 

P 

£ 

(a.  m.) 

11:40 

15 

12.50 

4.52 

0.5 

0.088 

.  .  .  .  

0.155 

0.57 

10 

12.60 

4.49 

0.5 

0.088 

0.154 

0.57 

10 

12.50 

4.52 

0.5 

0.088 

0.155 

(p.  m.) 

20 

12.50 

4.52 

0.7 

0.122 

0.155 

079 

VJr      ••"•_/ 

1:07 

20 

12.55 

4.51 

0.6 

0.104 

0154 

0.68 

90 

6.60 

8.57 

3.0 

0.532 

0.0073 

0.558 

90 

6.53 

8.66 

3.0 

0.532 

0.0071 

0.570 

1:13 

20 

6.39 

8.85 

2.6 

0.463 

0.595 

0.78' 

20 

6.43 

8.79 

23 

0.408 

0587 

0.70 

90 

6.48 

8.73 

3.0 

0.532 

0.0070 

0^579 

90 

6.45 

8.77 

3.0 

0.532 

0.0069 

0.584 

1:30 

10 

6.43 

8.79 

1.3 

0.233 

0.587 

0.40 

10 

6.43 

8.79 

1.7 

0.303 

0.587 

0.52 

90 

6.50 

8.70 

3.0 

0.532 

0.0070 

0.575 

90 

6.45 

8.77 

3.2 

0.566 

0.0074 

0.584 

15 

6.47 

8.74 

1.5 

0.268 

0.581 

0.46 

15 

6.47 

8.74 

1.9 

0.342 

0.581 

0^59 

90 

6.45 

8.77 

3.8 

0.664 

0.0086 

0.584 

90 

6.57 

8.61 

3.8 

0.664 

0.0090 

0.563 

5 

6.43 

8.79 

1.0 

0.176 

0.587 

0.30 

1:52 

5 

6.45 

8.77 

1.1 

0.195 

0.584 

0.33 

22 


EXPERIMENTS    IN    AERODYNAMICS. 


Collecting  the  values  of  km  from  the  several  days'  observations  and  reducing 
them  to  a  common  mean  temperature  of  10°  0.  and  pressure  of  735  mm.,  we 
have  the  following  summary  of  results : 

km 

August  27, 1888 •   0.00810 

28,     "    0.00794 

October  4,     "    0.00757 

The  observations  of  October  4  being  of  inferior  accuracy  to  the  others  on 
account  of  the  wind,  which  blew  in  sudden  gusts,  the  mean  of  the  first  two  days' 
experiments,  viz.,  km  =  0.0080,  may  be  considered  as  the  final  value  for  the 
coefficient  of  normal  pressure  resulting  from  the  experiments  with  this  instrument. 

The  columns  headed  Pw  =  0.0077  V2  in  the  experiments  of  August  27  and 
28,  and  PM  =  0.0076  V'1  in  the  experiments  of  October  4,  give  for  each  obser- 
vation of  the  inclined  plane  the  computed  pressure  which  thr>  plane  would 
sustain  if  moving  normally  with  its  velocity  F.  The  coefficient  adopted  for  the 
computation  is  the  mean  value  of  km,  resulting  from  the  experiments  of  the  day. 
The  last  column  of  the  tables  contains  the  ratio  of  the  actual  pressure  on  the 
inclined  plane  to  the  computed  pressure  on  the  normal  plane  given  in  the 
preceding  column. 

These  ratios  from  the  several  days'  experiments  are  collected  in  the  following 
summary,  and  mean  values  are  taken  for  the  different  angles  of  experiment. 
These  mean  ratios  are  plotted  in  Fig.  1,  and  a  smooth  curve  is  drawn  to  represent 
them. 

TABLE  V. — Summary  of  ratios  of  pressure  on  inclined  plane  to  pressure  on  normal  plane. 


Linear  velocity  of 
plane  (meters 
per  sec.). 

Angles  of  inclination. 

Remarks. 

45°       30° 

20° 

15° 

10° 

7J° 

5° 

4.5 

8.7 

11.2 

1.00 
0.95 

0.77 
0.82 

1.13* 

0.79 
0.80 
0.90 
0.95 

0.79 
0.87 
0.82 
0.84 
0.80 

.79 

.68 

.78 
.70 

.58 
.57 
.72 
.49 
.62 
.57 
.46 
.59 
.44 
.42 

.57f 

*  Omit. 
fGive  one-quarter  weight. 

.57f 
.40 
.52 

.24 
.24 
.44 
.35 

.23 
.30 
.26 
.33 

.30 
.33 



Mean 

0.89 

0.84 

.74 

.55 

.48 

.30 

.31 

IO& 


THE    RESULTANT   PRESSURE    RECORDER. 
FIG.  1. 


23 


9[ 


7( 


6C 


5( 


o 


3f 


2( 


l( 


30' 


5 


Ratio  of  the  total  normal  pressure  (Pa)  on  an  inclined  square  plane  to  the  pressure  (PM)  on 
a  normal  plane,  the  planes  moving  in  the  air  with  the  same  velocity. 

Abscissae.    Angles  of  inclination  («)  of  plane  to  horizon. 

p 
Ordinates.    ^-=z-P1(")  (expressed  as  a  percentage). 

"an 

Q  Represents  the  mean  of  observed  points  for  each  angle  of  experiment. 


24 


EXPERIMENTS   IN   AERODYNAMICS. 


The  values  in  the  tables  are  subject  to  a  correction  resulting  from  a  flexure 
in  the  balance-arm  and  its  support.  It  was  observed  (see  note  in  Table  111) 
that  the  trace  of  the  plane  set  at  90°  did  not  coincide  with  the  horizontal  (i.  e., 
the  perpendicular  to  the  vertical)  line  marked  on  the  trace,  but  was  uniformly  4° 
or  5°  below  it ;  so  that  the  angle  between  the  vertical  and  the  trace  of  the  plane 
did  not  measure  90°,  as  had  been  assumed,  but  uniformly  94°  or  95°,  the  average 
being  94°.6.  This  result  was  found  to  be  due  to  the  bending  backward  of  the 
balance-arm  and  its  support  by  the  pressure  of  the  wind,  while  the  recording 
board  and  plumb-line  presented  only  a  thin  edge  to  the  wind,  and  consequently 
remained  relatively  fixed.  During  motion,  therefore,  the  plane  actually  had  an 
inclination  to  the  horizon  about  5°  greater  than  the  angle  at  which  it  was  set  when 
at  rest.  This  flexure  seemed  to  obtain  for  all  angles  of  experiment,  but  with 
indications  of  a  slightly  diminishing  effect  for  the  smaller  ones ;  consequently 
the  pressure  ratios  above  given  for  angles  of  45°,  30°,  20°,  etc.,  really  apply  to 
angles  of  about  50°,  35°,  25°,  etc.  After  making  this  correction  the  final  result  of 
the  experiments  is  embodied  in  the  line  of  Fig.  1  designated  "corrected  curve."* 

At  the  inception  of  the  experiments  with  this  apparatus  it  was  recognized 
that  the  Newtonian  law,f  which  made  the  pressure  of  a  moving  fluid  on  an 
inclined  surface  proportional  to  the  square  of  the  sine  of  the  angle  between  the 
surface  and  the  current,  is  widely  erroneous,  though  it  is  still  met  in  articles 
relating  to  fluid  pressures,  and  vitiates  the  results  of  many  investigations  that 

*  The  ratios  given  by  the  "  corrected  curve  "  of  the  diagram  have  been  tabulated  for  angles  of  every  5°  and 
then  compared  with  all  the  experiments  and  formulae  with  which  I  am  acquainted.  Only  since  making  these 
experiments  my  attention  has  been  called  to  a  close  agreement  of  my  curve  with  the  formula  of  Duchemin, 
whose  valuable  memoir  published  by  the  French  War  Department,  Memorial  de  VArtitterie  No.  V,  I  regret  not 
knowing  earlier.  The  following  table  presents  my  values,  the  values  given  by  Duchemin's  formula,  and  a  column 
of  differences: 

Ratio  qftlte  total  pressure  (Pa  )  on  an  inclined  square  plane  to  the  pressure  (Pgo)  on  a  normal 
plane  moved  in  the  air  with  the  same  velocity. 


Pa 

p-  as  given  by  — 

Angles  of  inclination 
of  plane  to  direc- 
tion of  motion. 

Difference:  Duche- 
min  —  Langley. 

Experiments   with 
Resultant    Pres- 

Duchemin's formula  : 
2  sin  a 

sure  Recorder. 

1  +  sin'a 

5° 

.15 

.17 

+  .02 

10 

.30 

.34 

.04 

16 

.46 

.48 

.02 

20 

.60 

.61 

.01 

25 

.71 

.72 

.01 

30 

.78 

.80 

.02 

35 

.84 

.86 

.02 

40 

.89 

.91 

.02 

46 

.93 

.94 

.01 

t  Implicitly  contained  in  the  Principia,  Prop.  XXXIV,  Book  II. 


THE    RESULTANT   PRESSURE    RECORDER.  25 

would  otherwise  be  valuable.  Occasional  experiments  have  been  made  since  the 
time  of  Newton  to  ascertain  the  ratio  of  the  pressure  upon  a  plane  inclined  at 
various  angles  to  that  upon  a  normal  plane,  but  the  published  results  exhibit 
extremely  wide  discordance,  and  a  series  of  experiments  upon  this  problem 
seemed,  therefore,  to  be  necessary  before  taking  up  some  newer  lines  of  inquiry. 
The  apparatus  with  which  the  present  experiments  were  made,  was  designed 
to  give  approximations  to  the  quantitative  pressures,  rather  than  as  an  instru- 
ment of  precision,  and  its  results  are  not  expected  to  afford  a  very  accurate 
determination  of  the  law  according  to  which  the  pressure  varies  with  the  angle 
of  inclination  of  the  surface  to  the  current,  but  incidentally  the  experiments 
furnish  data  for  discriminating  between  the  conflicting  figures  and  formulae  that 
now  comprise  the  literature  of  the  subject.  We  may  remark  that  they  incident- 
ally show  that  the  effect  of  the  air  friction  is  wholly  insensible  in  such  experi- 
ments as  these;  but  the  principal  deduction  from  them  is  that  the  sustaining 
pressure  of  the  air  on  a  plane  1  foot  square,  moving  at  a  small  angle  of  inclina- 
tion to  a  horizontal  path,  is  many  times  greater  than  would  result  from  the 
formula  implicitly  given  by  Newton.  Thus  for  an  angle  of  5°  this  theoretical 
vertical  pressure  would  be  sin2  5°cos  5°  =  0.0076  of  the  pressure  on  a  normal 
plane  moving  with  the  same  velocity,  while  according  to  these  experiments  it  is 
in  reality  0.15  of  that  pressure,  or  twenty  times  as  great  as  the  theoretical  amount 


CHAPTER   V. 

THE    PLANE-DROPPER. 

It  is  so  natural  to  suppose  that  to  a  body  falling  in  the  air  under  the 
influence  of  gravity,  it  is  indifferent  whether  a  lateral  motion  is  impressed  upon 
it  or  not,  as  regards  the  time  of  its  fall,  that  we  may  sometimes  find  in  elemen- 
tary text-books  the  statement  that  if  a  ball  be  shot  from  a  cannon  horizontally, 
at  any  given  height  above  the  ground,  and  if  a  ball  be  dropped  vertically  at  the 
same  instant  with  the  discharge,  the  two  projectiles  will  reach  the  ground  at  the 
same  time,  and  like  illustrations  of  a  supposed  fact  which  has  in  reality  no 
justification  in  experience.  According  to  the  experiments  I  am  about  to  describe, 
this  cannot  be  the  case,  although  it  requires  another  form  of  projectile  to  make 
the  difference  in  the  time  of  fall  obvious. 

It  is  shown  by  the  following  experiments  that  if  a  thin  material  plane  be 
projected  in  its  own  plane  horizontally,  it  will  have  a  most  conspicuously  different 
time  of  falling  according  to  the  velocity  of  its  lateral  translation  ;  and  this  time 
may  be  so  great  that  it  will  appear  to  settle  slowly  down  through  the  air,  as  it 
might  do  if  almost  deprived  of  weight,  or  as  if  the  air  were  a  highly  viscous 
medium,  the  time  of  fall  being  (it  will  be  observed)  thus  prolonged,  when  there 
is  no  inclination  of  the  plane  to  the  horizon — a  noteworthy  and  unfamiliar  fact,* 
which  is  stated  here  on  the  ground  of  demonstrative  experiment.  The  experi- 
mental quantitative  demonstration  of  this  important  fact,  is  the  primary  object 
of  the  instrument  I  am  about  to  describe,  used  with  the  horizontal  plane.  It  is, 
of  course,  an  entirely  familiar  observation  that  we  can  support  an  inclined  plane 
by  moving  it  laterally,  deriving  our  support  in  this  case  from  the  upward  com- ' 

*  An  analogous  phenomenon  concerning  the  movement  of  one  solid  over  another  yielding  one,  such  as  when 
"  Swift  Camilla  scours  the  plain, 

"  Flies  o'er  the  unbending  corn,  and  skims  along  the  main ; " 

or  in  the  familiar  illustration  of  the  skater  on  thin  ice,  or  in  the  behavior  of  missiles  like  the  boomerang,  has 
long  been  observed ;  and  yet,  remarkable  as  its  consequences  may  be,  these  seem  to  have  attracted  but  little 
attention.  Neither  has  the  analogy  which  it  is  at  least  possible  may  exist  between  this  familiar  action  of  the  skater 
upon  the  i,ce  and  of  the  potential  flying-machine  in  the  air  been  generally  observed  till  lately,  if  at  all — at  least, 
so  far  as  I  know,  the  first  person  who  has  seemed  to  observe  the  pregnant  importance  of  the  illustration  is 
Mr.  Wenham,  whom  I  have  already  alluded  to.  I  do  not,  then,  present  the  statement  in  the  text  as  a  fact  in 
itself  unpredictable  from  experience,  for  it  is  a  familiar  fact  that  the  air,  like  every  material  body,  must  possess 
inertia  in  some  degree.  It  is  the  quantitative  demonstration  of  the  extraordinary  result  of  this  inertia  which 
can  be  obtained  with  simple  means  in  causing  the  thin  air  to  support  objects  a  thousand  times  denser  than 
itself,  which  I  understand  to  be  at  the  time  I  write,  both  unfamiliar  in  itself,  and  novel  in  its  here  shown  con- 
sequences. 

(26) 


THE    PLANE-DROPPER.  27 

ponent  of  pressure  derived  from  the  wind  of  advance ;  but,  so  far  as  I  am  now 
aware,  this  problem  of  the  velocity  of  fall  of  a  horizontal  plane  moving  hori- 
zontally in  the  air  has  never  been  worked  out  theoretically  or  determined  experi- 
mentally, and  I  believe  that  the  experimental  investigation  whose  results  I  am 
now  to  present  is  new. 

With  all  the  considerations  above  noted  in  view,  I  have  devised  a  piece  of 
apparatus  which,  for  distinction,  I  will  here  call  the  Plane- Dropper,  intended,  in 
the  first  place,  to  show  that  a  horizontal  plane  in  lateral  motion  requires  an 
increased  time  for  its  descent ;  second,  to  make  actual  measurement  of  the  time 
of  fall  of  variously  shaped  planes  and  to  give  at  least  the  first  approach  to  the 
procuring  of  the  quantitative  data ;  third,  to  connect  these  experiments  with  those 
immediately  allied  to  them,  where  the  plane  has  an  inclination  to  the  horizon ; 
and,  fourth,  to  make  experiments  to  show  the  depth  of  the  air  strata  disturbed  by 
the  moving  plane  during  the  time  of  its  passage. 

Drawings  of  the  Plane- Dropper  are  given  in  plate  VI.  F  is  a  vertical  iron 
frame  with  a  wooden  back  WW,  which  is  shown  fastened  by  bolts  B  to  the 
end  of  the  arm  of  the  turn-table.  The  fourth  side  of  the  rectangle  is  a  planed 
brass  frame  on  which  an  aluminum  falling-piece  runs  up  and  down  on  friction 
rollers.  The  plate  contains  enlarged  front  and  side  views  of  the  falling-piece, 
and  a  section  of  the  brass  frame  and  falling-piece,  showing  the  arrangement  of 
the  ebonite  friction  rollers.  By  means  of  the  clamps  CO'  the  falling-piece  carries 
two  wooden  planes,  which  may  be  set  by  the  clamps  DD'  horizontal,  or  at  any 
angle  with  the  horizon  up  to  45°.  Guy  lines  extend  from  the  top  and  bottom  of 
the  falling-piece  to  the  outer  edges  of  the  planes  and  keep  them  from  bending. 
A  detent  at  the  top  of  the  frame  holds  the  falling-piece  until  released  at  any 
desired  instant  by  the  action  of  an  electro- magnet,  M.  A  spring  cushion,  S,  at 
the  bottom  of  the  frame,  breaks  the  force  of  the  fall. 

Provision  is  made  for  setting  the  brass  frame  vertical,  and  by  means  of  the 
handle  H  the  frame  can  be  revolved  180°  about  its  vertical  axis,  so  as  to  present 
successively  one  side  or  the  other  side  to  the  wind  of  advance,  and  thus  to  eliminate 
any  defect  in  setting  the  wings  absolutely  horizontal,  or  any  inequality  in  the 
instrument  not  otherwise  suspected. 

The  total  fall  is  four  feet,  and  the  total  time  of  fall  is  registered  electrically 
by  means  of  contact-pieces  a  and  e,  near  the  top  and  bottom  of  the  frame.  As 
soon  as  released,  the  aluminum  falling-piece  presses  the  contact-piece  a  against 
the  frame  and  completes  the  circuit.  While  falling,  the  circuit  is  open,  and  at 
the  distance  of  four  feet  the  contact-piece  e  is  pressed  against  the  frame  and  the 
circuit  is  again  closed.  In  November,  1890,  three  additional  contact-pieces, 
b,  c,  d,  were  added,  so  as  to  measure  the  time  of  fall  through  each  successive  foot. 
The  registration  is  made  on  the  stationary  chronograph,  together  with  that  of 


28  EXPERIMENTS    IN   AERODYNAMICS. 

the  quadrant  contacts  of  the  turn-table,  the  currents  for  the  moment  being  cut 
off  from  the  quadrant  contacts  and  sent  through  the  Plane- Dropper. 

The  dimensions  and  weight  of  the  principal  parts  of  the  apparatus  are  as 
follows : 

Length  of  brass  tube 160  centimeters. 

Length  of  aluminum  falling-piece 25 

Length  of  buffers 5  " 

Actual  distance  of  fall  (between  contacts) 122  " 

Distance  of  center  of  brass  frame  and  falling-piece  from  center  of 

turn-table,  when  mounted 981  " 

Weight  of  falling-piece 350  grammes. 

The  planes  are  made  of  varnished  pine  about  2imm.  thick,  and  stiffened  on 
one  edge  with  an  aluminum  strip. 

Five  different  pairs  were  used,  having  the  following  dimensions  and 
weights : 

(1)  Two  planes,  each  *6  x  12  in.  (15.2  x  30.5  cm.) ;  weight  of  pair,  123  grammes. 

(2)  "  "  "8x9  in.  (22.9  x  20.3  cm.) ;  "  115  " 

(3)  "  "  "     12  x   6  in.  (30.5  x  15.2  cm.) ;  "  "  114  " 

(4)  "  "  "     18  x   4  in.  (45.7  x  10.2  cm.) ;  "  114  " 

(5)  "  "  "     15  x   4  in.  (38.1  x  10.2  cm.) ;  "  118  " 

Each  pair  of  planes,  therefore,  except  the  last,  has  an  area  of  one  square 
foot,  and  weighs,  with  the  aluminum  falling-piece,  approximately  one  pound. 

It  may  be  desirable  to  add  that  this  instrument  was  constructed  with  special 
pains  in  all  the  circumstances  of  its  mechanical  execution,  the  very  light  falling- 
piece,  for  instance,  moving  on  its  friction  wheels  so  readily  that  it  was  not 
possible  to  hold  the  rod  in  the  hands  sufficiently  horizontal  to  keep  the  "  falling- 
piece"  from  moving  to  one  end  or  the  other,  like  the  bubble  of  a  level  held  in 
the  same  manner. 

Preliminary  experiments  were  made  to  determine  the  effects  of  friction  on 
the  time  of  fall,  when  the  Plane- Dropper  is  in  rapid  horizontal  motion,  by  drop- 
ping the  aluminum  falling-piece  without  planes  attached,  and  it  was  found  that 
under  these  circumstances  the  time  of  fall  is  not  sensibly  greater  when  in  rapid 
motion  than  when  at  rest.  As  a  further  test,  the  planes  were  then  attached  to 
the  falling-piece  in  a  vertical  position,  that  is,  so  as  to  present  their  entire  surface 
to  the  wind  of  rotation,  and  thus  to  produce  a  friction  very  much  greater  than  any 
occurring  in  the  subsequent  experiments ;  but  the  time  of  fall  was  not  increased 
to  any  notable  degree.  The  effect  of  friction  and  other  instrumental  errors  are 
shown  thus,  and  by  considerations  already  presented,  to  be  negligible  in  com- 
parison with  the  irregularities  inevitably  introduced  by  irregular  air  currents 

*  First  measurement  refers  to  advancing  edge. 


THE    PLANK-DROPPER. 


29 


when  the  whirling  table  is  in  motion,  which  appear  in  the  observations.  The 
probable  error  of  the  measured  time  of  falling  in  still  air,  when  only  instrumental 
errors  are  present,  is  within  T£<J  of  a  second. 

The  first  series  of  experiments  with  horizontal  planes  was  made  May  25 
and  June  10  to  June  14,  1889,  and  was  devoted  to  the  first  two  objects  already 
set  forth,  namely : 

1st.  To  show  by  the  increased  time  of  fall  that  the  supporting  power  of  the 
air  increases  with  the  horizontal  velocity  rf  the  body ;  and, 

2d.  To  get  first  approximations  to  the  times  of  falling  of  rectangular  planes  of 
different  shapes  and  aspects,  the  latter  condition  having  reference  to  whether  the 
long  or  the  short  side  of  the  rectangle  is  perpendicular  to  the  direction  of  advance. 

An  abstract  of  the  note  book  for  June  11,  1889,  is  given  here  as  an  example 
of  the  detailed  records  made  in  these  experiments. 

JUNE  11, 1889. — S.  P.  LA.NGLEY,  Conducting  experiments  and  recording;  P.  W.  VERY,  Assisting. 

Notes :  "A"  and  "  B  "  designate  the  direct  and  reversed  positions  of  the  brass  frame  and  falling 
piece ;  belt  on  third  pulley. 

To  determine  time  of  falling. 


•oa^- 

£P 

£  ^l: 
S 

3^ 

Size  and  attitude  of  planes. 

"sgl 

•si 

Jil 

<u  JD, 

13  x  4-inch  planes  horizontal  

38 

A  1  30 

3.8 

A  1.15 

3.75 

B1.20 

4.25 

B1.15 

12  x  6-inch  planes,  horizontal  : 

At  rest  (in  open  air)  

052 

tt      '    tt        it 

052 

it          tt        it 

052 

tt          it        tt 

In  motion  on  turn-table    .  .  . 

6.0 

B0.71 

tt            tt            tt 

6.2 

B0.80 

it            a            tt 

6.1 

A  0.76 

it            a            it 

6.1 

A  0.80 

tt            tt            it 

3.5 

A  1.00 

The  detailed  observations  with  the  five  different  planes  already  described 
are  contained  in  Tables  VI  and  VII,  and  the  results  are  presented  graphically 
in  figure  2,  where  the  times  of  fall  are  plotted  as  ordinat.es,  and  abscissae  are 
horizontal  velocities  of  translation. 


30 


EXPERIMENTS    IN    AERODYNAMICS. 

TABLE  VI— MAY  25,  1889. 

To  find  the  time  of  fall  of  different  planes;  plane-dropper  statioua;y. 

S.  P.  LANGLEY,  Conducting  experiments;  F.  W.  VERY,  Assisting. 

Barometer,  731.5  mm. ;  temperature,  17°.5  C. ;  wind,  light. 


Weight  (with  dropping  piece). 

Time  of  fall  of 

Size  of  planes. 

Angle  with         4  feet   (1.22 
horizon.           meters). 

(Grammes.) 

(Pounds.) 

(Seconds.) 

One  pair  12  x  6  inches  (30.5  x  15.2 

464 

1.02 

0° 

0.58 

cm.). 

0 

0.58 

is     .      22 

0 

0.52 

«|        ~~Wr       1® 

45 

0.54 

12.       '        22 

45 

0.55 

One  pair  18  x  4  inches  (45.7  x  10.2 

464 

1.02 

0 

0.54 

cm.). 

0 

0.55 

45 

0.55 

Result:  The  time  of  fall  of  both  planes,  at  angles  both  of  0°  and  45°,  is,  approximately,  0.55 

seconds. 

TABLE  VII— JUNE  10,  11,  12,  AND  14, 1889. 

S.  P.  LANGLEY,  Conducting  experiments;  F.  W.  VERY,  Assisting. 

Mean  barometer,  734.0  mm.;  mean  temperature,  June  10,  26.6°  C. ;  June  11,  17.8°  C. ;  June  12, 

21.1°  C. ;  June  14,  26.1°  C. 


To  determine  the  times  of  fall  of  horizontal  planes  endowed  with 
horizontal  velocity. 

To  determine  the  horizontal  velocities 
at  which  inclined  planes  are  sup- 
ported by  the  air. 

jj{ 

o  <3 

,2  ft 

<D 

^  —  s 

1. 

<B          ° 

r2      ft 

Dimensions  and  aspect 
of  plane. 

Date. 

1.85 

lit 

"8  § 

Date. 

*  1 

as  8 

O            00 

it? 

III 

i*i 

<D 

a 

H 

all 

.S  t>^  § 
o  .t3  « 

EH 

W 

P 

< 

P 

M 

1889. 

1889. 

is        f        is 

June  10 

0.00 
5.70 
5.90 

0.0 

10.8 
10.4 

0.53 
0.70 
0.65 

June  10 

tt 

16° 
5 

5.1 
3.4 

12.1 
18.1 

*l               -Wr              I* 

is         \        is 

" 

3.35 

18.4 

1.62 

18x4  inches  (45.7x10.2 

u 

3.45 

17.9 

1.65 

cm.). 

u 

5.80 

10.6 

0.85 

Weight,   1.02   Ibs.   (464 

" 

4.35 

14.2 

0.90 

grammes). 

u 

3.75 

16.4 

1.08 

Radius  of  rotation  to  cen- 

June 11 

3.80 

16.2 

1.30 

June  11 

20° 

6.0 

10.3 

ter  of  planes,  9.81  m. 

u 

3.80 

16.2 

1.15 

15 

6.2 

9.9 

THE   PLANE-DROPPER. 
TABLE  VII — Continued. 


31 


oh^ 

£! 

i 

t 

o^ 

£  e, 

O 

>  2 

^ 

-1 

Q 

>  2 

Dimensions  and 
of  plane. 

aspect 

Date. 

w  ',  |    rj 

fi    0    0 

ill 

--3-S     • 

!i| 

53  o 

o 

Date. 

ti-.  fl 

*J 

& 

S,  Q* 

N             ^ 

Si5  +i 

o  "S  01 

i 

c? 

S  r3   ^ 

"C  .S*  QJ 
O  -rH     QD 

H 

W 

•5 

P 

K 

1889. 

1889. 

76           f 

is 

June  11 

3.75 

16.4 

1.20 

June  11 

3J° 

3.3 

18.7 

** 

4.25 

14.5 

1.15 

7S 

is 

June  12 

3.00 

20.5 

1.95 

June  12 

3 

3.35 

18.4 

u 

3.60 

17.1 

1.50 

u 

2 

2.85 

21.6 

18x4  inches  (45.7x10.2 

1 

3.00 

20.5 

2.55 

cm.). 

t 

3.05 

20.2 

2.68 

Weight,   1.02   Ibs.    (464 

t 

3.10 

19.9 

2.75 

grammes). 

{ 

3.15 

19.6 

2.05 

t 

3.70 

16.8 

1.65 

12       i 
,  1  * 

.    *2    . 

« 

0.00 

0.0 

0.56 

June  11 

25° 

5.6 

11.0 

"LZJ 

£ 

_r 

" 

6.15 

10.0 

0.80 

« 

6 

3.8 

16.2 

12       \ 

^~Ti 

r-1 

" 

6.05 

10.2 

0.74 

June  12 

5 

3.3 

18.7 

June  11 

3.50 

17.6 

1.00 

12x6  inches  (30.5x15.2 

" 

3.40 

18.1 

1.16 

cm.) 

June  12 

2.87 

21.4 

1.29 

Weight,  464 

grammes. 

" 

2.82 

21.9 

1.59 

8 

8 

u 

0.0 

0.57 

tt 

25° 

6.0 

10.3 

i 

« 

13.15 

4.7 

0.62 

u 

15 

4.9 

12.6 

°i 

J- 

05 

" 

3.50 

17.6 

0.72 

1! 

12 

4.2 

14.7 

a 

a 

tf 

2.85 

21.6 

0.82 

u 

6 

2.9 

21.2 

tt 

2.65 

23.3 

0.86 

Weight,  465 

grammes. 

6     i 

6 

u 

0.0 

0.57 

30° 

5.9 

10.5 

I 

(t 

11.65 

5.3 

0.58 

20 

5.0 

12.3 

&i          r 

S         I- 

M 

ft 

4.10 

15.0 

0.65 

15 

4.2 

14.7 

(1 

5.10 

12.1 

0.70 

13 

3.8 

16.2 

6 

G 

ft 

2.78 

22.2 

0.72 

9 

2.9 

21.2 

6x12  inches. 

Weight,  473 

grammes. 

is 

L 

IS 

June  14 

5.65 

10.9 

0.76 

June  14 

20° 

5.25 

11.7 

fel 

1* 

1 

u 

3.10 

19.9 

1.28 

ct 

15 

5.10 

12.1 

L                        i' 

15 

I1  — 

u 

3.00 

20.5 

1.28 

a 

15 

4.65 

13.3 

15x4  inches  (38. 

^ 

1  x  10.2 

' 

10 

7 

4.55 
3.85 

13.6 
16.0 

cm.). 
Weight,  468 

grammes. 

5 
4 

3.30 
3.10 

18.7 
19.9 

32 


EXPERIMENTS    IN    AERODYNAMICS. 
FIG.  2. 


225 


2.00 


175 


1.50 


1.25 


1.00 


0.75 


MOJ 


iggram  a 


Plane, 


10 


15 


20 


ISO 


125 


100 


0.75 


1.75 


1.50 


1.25 


1.00 


0.75 


0.50 


B 


0 


10 


IS 


20 


Times  of  falling  4  feet  of  horizontal  planes  on  the  Plane-Dropper. 
Average  weight  of  planes  =  465  grammes. 

Abscissas :  —  Horizontal  velocities  of  translation  in  meters  per  second. 
Ordinates :  =  Times  of  fall  in  seconds. 


THE    PLANE-DROPPER.  33 

Perhaps  the  most  important  primary  fact  exhibited  by  these  experiments 
is  that  the  time  of  fall  for  horizontal  planes  of  all  shapes  is  greater  as  tho 
horizontal  velocity  increases,  and  also  (as  the  form  of  the  curves  shows)  that  this 
retardation  in  the  velocity  of  falling  goes  on  at  an  increasing  rate  with 
increasing  velocities  of  translation. 

Secondly,  we  see  that  those  planes  whose  width  from  front  to  back  is  small 
in  comparison  with  the  length  of  the  advancing  edge  have  a  greater  time  of 
fall  than  others.  This  difference  is  uniform  and  progressive  from  the  6  x  12 
inch  planes  to  the  18  x  4  inch  planes.  Expressing  this  advantage  quantitatively, 
the  curves  show  that  the  planes  having  an  advancing  edge  of  6  inches  and 
a  width  of  12  inches  from  front  to  back,  when  they  have  a  horizontal  velocity 
of  20  meters  per  second,  fall  the  distance  of  4  feet  in  0.7  second,  while  planes 
of  the  same  area  and  weight  having  the  advancing  edge  18  inches  and  4  inches 
from  front  to  back,  when  moving  with  the  same  velocity,  are  upheld  to  such  an 
extent  that  their  time  of  fall  is  2  seconds.  This  interesting  comparative  result  is 
also  indirectly  valuable  in  giving  additional  evidence  that  the  largely  increased 
time  of  fall  of  the  better-shaped  planes  at  the  high  speeds  is  not  due  to  the  lateral 
friction  of  the  falling-piece  against  the  frame.  The  friction  with  the  6  x  12  inch 
planes  is  as  great  as  vvitli  any  of  the  others,  yet  their  time  of  falling  is  only 
slightly  greater  at  high  speeds  than  at  rest.  Attention  is  called  to  the  fact  that 
at  the  highest  velocity  attained  in  the  present  series  of  experiments,  20  meters 
per  second,  the  curve  shows  that  the  time  of  falling  of  the  18  x  4  inch  planes  was 
increasing  very  rapidly,  so  much  so  as  to  make  it  a  subject  of  regret  that  the 
slipping  of  belts  prevented  experiments  at  still  higher  speeds.  We  may,  however, 
reasonably  infer  that  with  a  sufficient  horizontal  velocity,  the  time  of  fall  may  be 
prolonged  to  any  assigned  extent,  and  that  for  an  infinite  velocity  of  translation, 
the  time  of  fall  will  be  infinite,  or,  in  other  words,  that  the  air  will  act  as  a  solid 
support. 

In  may  be  of  interest  to  connect  these  observations  with  some  partly  analogous 
facts  which  are  more  familiar. 

It  is  frequently  observed  that  a  sheet  of  very  thin  ice  will  bear  up  a  skater 
if  he  is  in  rapid  motion  which  would  not  sustain  his  weight  if  he  were  still ;  and 
even  if  we  neglect  the  slight  difference  of  specific  gravity  between  water  and 
ice,  and  suppose  the  latter  to  have  no  differential  buoyancy,  the  rapid  skater 
will  still  be  able  to  pass  safely  over  ice  that  would  not  bear  his  weight  if  he 
were  at  rest ;  for  while  his  mass  is  the  same  in  both  cases,  that  of  the  ice  called 
into  play  in  sustaining  him  is  only  that  corresponding  to  one  unit  of  area  when 
he  is  at  rest,  but  to  many  when  he  is  moving. 

In  this  form  of  explanation  and  illustration  the  attention  is  directed  only  to 
the  action  of  the  air  beneath  the  plane,  but  in  fact  the  behavior  of  the  air  above 

5 


34  EXPERIMENTS    IN    AERODYNAMICS. 

the  plane  is  of  perhaps  equal  importance,  and  its  action  has  been  present  to  my 
mind  throughout  these  experiments,  although  for  the  purpose  of  concise  exposition 
only  the  former  is  here  referred  to.  By  analogous  reasoning  in  the  case  of  a 
heavy  body  immersed  in  any  continuous  fluid,  even  gaseous,  while  the  mass 
of  air  or  gas  whose  inertia  is  called  into  action  is  small  and  affords  a  slight 
sustaining  power  when  the  body  is  at  rest,  it  becomes  greatly  multiplied  with 
lateral  motion,  and  the  more  rapid  this  lateral  motion,  the  greater  will  be  the 
sustaining  action  of  the  fluid.  So,  then,  in  the  case  of  any  heavy  body  which 
will  fall  rapidly  in  the  air  if  it  fall  from  rest,  the  velocity  of  fall  will  be  more 
and  more  slow  if  the  body  be  given  successively  increasing  velocities  of  lateral 
translation  and  caused  to  run  (so  to  speak)  upon  fresh  masses  of  air,  resting  but 
a  moment  upon  each. 

The  above  analogy,  in  spite  of  its  insufficiency  as  regards  the  effect  of  elas- 
ticity, is  useful,  and  may  be  further  extended  to  illustrate  the  relative  results 
obtained  with  the  differently  shaped  planes  and  with  the  same  plane  under 
different  "  aspects ;  "  thus  the  action  on  the  air  of  a  plane  whose  advancing  edge 
is  twice  its  lateral  edge — e.  g.,  the  12x6  inch  plane,  with  12-inch  side  foremost — 
may  be  compared  to  that  of  two  skaters  side  by  side,  each  advancing  over  his  own 
lines  of  undisturbed  ice  ;  but  the  same  plane  with  the  6-inch  side  foremost,  to  the 
same  skaters,  when  one  is  behind  the  other,  so  that  the  second  is  passing  over  ice 
which  has  already  yielded  to  the  first  and  is  partly  sinking. 

The  second  series  of  experiments,  made  on  the  same  dates  as  the  first,  was  to 
cover  the  third  object  of  experiment — that  is,  to  determine  for  different  angles  of 
inclination  what  speed  is  necessary  in  order  to  derive  an  upward  thrust  just 
sufficient  for  sustaining  the  planes. 

The  results  of  these  two  series  of  experiments  furnish  all  that  is  needed  to 
completely  elucidate  the  proposition  that  I  first  illustrated  by  the  suspended 
plane,  namely,  that  the  effort  required  to  support  a  bird  or  flying  machine  in  the 
air  is  greatest  when  it  is  at  rest  relatively  to  the  air,  and  diminishes  with  the 
horizontal  speed  which  it  attains,  and  to  demonstrate  and  illustrate  the  truth  of 
the  important  statement  that  in  actual  horizontal  flight  it  costs  absolutely  less 
power  to  maintain  a  high  velocity  than  a  low  one.  It  has  already  been  explained 
that  when  the  planes  have  such  an  angle  of  elevation  and  such  a  horizontal 
velocity  that  they  first  rise  from  their  support  and  are  then  with  a  slightly 
diminished  velocity  just  sustained  without  falling,  they  are  said  to  "  soar,"  and 
the  corresponding  horizontal  velocity  is  called  "  soaring  speed."  Attention  has 
already  been  called  to  the  importance  thus  attachable  to  the  word  "  horizontal  " 
as  qualifying  flight,  and  implying  its  most  economic  conditions,  when  no  useless 
work  is  expended. 


THE    PLANE-DROPPER. 


35 


The  actual  mode  of  experiment  with  the  inclined  planes  was  to  set  the  plane 
at  a  given  angle  of  elevation,  for  example  5°,  and  approximate  to  the  critical 
soaring  speed  by  gradual  variations  of  velocity,  both  above  and  below  it.  The 
following  extract  from  the  note  book  shows  the  character  of  the  record  made  in 
executing  this  experiment : 

12  x  6  inch  planes,  inclined. 


Angle  of  inclination. 

Time  of  1  revolution 
of  turn-table 
(seconds). 

Attitude  of  plane. 

25° 
6 

5.6 
3.8 

Soaring. 

« 

18  x  4  inch  planes,  inclined. 


_c 

111 

^+-4     O 

<«  °v3 

.Attitude  of  plane. 

Estimated  result. 

O  '[^ 

°  §  ® 

rt 

<; 

I-"9 

4° 

34 

More  than  soaring  

f  For  angle  3i°,  soaring  speed 

=  1  rev- 

3 

32 

Not  quite  soarin0'  

{     olution  in  3.3  seconds. 

20 

6.0 

Soaring. 

15 

55 

f  For  angle  15°  soaring  speed 

=  1  rev- 

15 

68 

Not  quite  soaring  

1      olution  in  6.2  seconds. 

The  detailed  observations  have  already  been  given  in  Tables  VI  and  VII 
and  the  results  are  plotted  in  Figure  3,  in  which  the  ordinates  are  soaring  speeds 
and  the  abscissae  are  the  corresponding  angles  of  inclination  of  the  planes  to  the 
horizon.  This  diagram  shows  that  when  set  at  an  angle  of  9°  the  6  x  12  inch 
plane  requires  a  horizontal  velocity  of  21.2  meters  per  second  to  sustain  it  in  the 
air,  while  the  18  x  4  inch  plane,  set  at  the  same  angles,  is  supported  by  the  air 
when  it  is  driven  at  a  velocity  of  only  14  meters  per  second.  The  work  to  be 
done  in  maintaining  the  flight  at  14  meters  per  second  is  less  than  one-half  that 
for  21.2  meters  per  second,  the  angle  remaining  the  same. 

These  experiments  enable  us  to  make  a  first  computation  of  the  work  expended 
in  horizontal  flight.  Let  us,  then,  determine  the  horse-power  required  to  drive 
the  two  18  x  4  inch  planes  horizontally  in  the  air,  when  the  planes  are  inclined 
successively  at  9°  and  at  5°.  The  work  done  per  second  is  given  by  the  product 
E  X  V,  B  being  the  horizontal  component  of  pressure  on  the  plane,  and  V  the 


36 


EXPERIMENTS    IN    AERODYNAMICS. 
FIG.  3. 


Velocities  of  soaring  of  inclined  planes  on  the  Plane-Dropper. 
Average  weight  of  plane  —  465  grammes. 
Abscissae :  =  Angles  of  inclination  (a)  of  plane  to  horizon. 
Ordinates :  =  Velocities  in  meters  per  second. 


THE    PLANE-DROPPER. 


37 


soai-ing  speod.  From  Fig.  3  we  find  that  the  soaring  velocities  corresponding 
to  these  angles  are  respectively  14  and  17.2  meters  per  second. 

Taking  the  vertical  component  of  pressure  as  equal  to  the  weight  of  the  plane, 
464  grammes,  which  relation  obtains  at  soaring  speed,  the  horizontal  component 
of  pressure,  or  the  resistance  to  advance,  is  given  by  the  formula  : 

R  =  464  tan  9°  ==  73.3  grammes,  for  9°; 
R  =  464  tan  5°  =  40.6  grammes,  for  5°, 

a  formula  which  is  immediately  derived  from  the  fundamental  principles  of 
mechanics  and  appears  to  involve  no  assumption  whatever.  The  work  done  per 
minute,  R  X  V,  is  62  kilograrnmeters  (450  foot-pounds)  for  9°,  and  43  kilogram- 
meters  (312  foot-pounds)  for  5°.  For  the  former  case  this  is  0.0156  horse-power, 
and  for  the  latter  case,  approximately  0.0095  horse-power  ;  that  is,  less  power  is 

FIG.  4. 


$.  riffle  pear  ofplane,  1. 


io  id.o  iSc  zoo 

Times  of  falling  4  feet  of  single  and  double  pairs  of  15  x  4  inch  planes. 
Abscissae :  Horizontal  velocities  of  translation  in  meters  per  second. 
Ordinates :  Time  of  fall  in  seconds. 

required  to  maintain  a  horizontal  velocity  of  17  meters  per  second  than  of  14;  a 
conclusion  which  is  in  accordance  with  all  the  other  observations  and  the  general 
fact  deducible  from  them,  that  it  costs  less  power  in  this  case  to  maintain  a  high 
speed  than  a  low  one — a  conclusion,  it  need  hardly  be  said,  of  the  very  highest 
importance,  and  which  will  receive  later  independent  confirmation. 

Of  subordinate,  but  still  of  very  great,  interest  is  the  fact  that  if  a  larger 
plane  have  the  supporting  properties  of  this  model,  or  if  we  use  a  system  of 
planes  like  the  model,  less  than  one-horse  power  is  required  both  to  support  in 
the  air  a  plane  or  system  of  planes  weighing  100  pounds,  and  at  the  same  time 
to  propel  it  horizontally  at  a  velocity  of  nearly  40  miles  an  hour. 


38 


EXPERIMENTS    IN    AERODYNAMICS. 


The  third  series  of  experiments  made  with  the  plane-dropper  is  designed 
to  investigate  the  effect  of  two  sets  of  planes,  one  above  the  other.  For  this 
purpose  the  planes  and  falling  piece  are  so  weighted  that  the  previous  ratio  of 
weight  to  surface  is  retained ;  that  is,  in  the  previous  case  the  weight  is  1  pound 
to  1  square  foot  of  surface,  and  with  the  double  set  of  planes  the  weight  is 

Experiments  with  two  sets  of  planes,  one  above  the  other. 
TABLE  VIII.— JUNE  14,  1889. 


To  determine  the  times  of  fall  of  a  system  of  horizontal  planes 
endowed  with  horizontal  velocity. 

To  determine  the  horizontal  velocities  at 
which  a  system  of  inclined  planes  will 
be  supported  by  the  air. 

lit 

•i!4 

1 

I 

II! 

Horizontal  velocity. 

_      o 

^  s 

! 

S 

o>       ° 

. 

^ 

Qj  f  |  t    p\ 

<D 

S*i  5 

Dimensions  and  aspect  of  plane. 

fi    O    O> 
O            00 

•f  i^ 

Si 

T3  5< 

C    O    OJ 

O        tn 

Vn    C  ^ 

^ 

0^ 

"8  §  « 

9   ^*  £3 

0    0 

o 

0    O^J 

J£* 
Q 

~  0 

C?  "•£*  _Q 

—    ^,  O 

0 

9 

p—  < 

o'-S^ 

O>    o 

8,33 

*Vi  -tj**  QJ 

O   -*rH      OJ 

s 

M 

JAJ 

kS     QQ 

&J   ^ 

H 

w 

EH 

< 

H 

P 

15         f        IS 

3.1 

19.9 

0.90 

10° 

4.33 

14.2 

46.7 

'[  iKrt  P 

8 

3.85 

16.0 

'52.5 

IS                     JS 

6 

3.48 

17.7 

58.1 

15  x  4  inches  (38.1  x  10.2  cm.). 

6 

3.35 

18.4 

60.3 

Double  pair  of  planes,  2  inches 

5 

Did  not 

rise. 

(5.1  cm.)  apart. 

Total  weight  of  planes  and  falling- 

piece,  942  grammes. 

Same  planes,  4  inches  (10.2  cm.) 
apart. 

7.30 
3.13 

8.4 
19.7 

0.73 
1.36 

15 
10 

5.30 
4.65 

11.6 
13.3 

38.1 
43.5 

10 

4.65 

13.3 

43.5 

7 

3.38 

18.2 

59.8 

5 

3.33 

18.5 

60.7 

4 

3.33 

18.5 

60.7 

4 

3.27 

18.9 

61.8 

Same  planes,  6  inches  (15.2  cm.) 

5.88 

10.5 

0.73 

20(?) 

5.60 

11.0 

36.1 

apart. 

2.78 

22.2 

1,34 

15 

5.40 

11.4 

37.4 

0.00 

0.0 

0.55 

10 

4.55 

13.5 

44.4 

2.65 

23.3 

1.60 

7 

3.95 

15.6 

51.2 

5 

3.45 

17.9 

58.6 

5 

3.45 

17.9 

58.6 

4 

2.93 

21.0 

69.0 

4 

2.95 

20.9 

68.5 

2J 

2.85 

21.6 

71.0 

made  2  pounds  to  2  square  feet.  The  preceding  experiments,  made  with  the 
single  pair  of  15  x  4  inch  planes,  were  then  repeated  on  June  14,  with  a  double 
pair  of  planes  placed  at  distances  of  2,. 4,  and  6  inches  apart.  The  detailed 
observations  are  given  in  Table  VIII.  The  times  of  falling  are  plotted  in  Fig.  4. 
The  soaring  speeds  are  plotted  in  Fig.  5,  without  attempting  to  smooth  out  the 


THE    PLANE-DROPPER. 
PIG.  5. 


Velocities  of  soaring  of  single  and  double  pairs  of  15  x  4  inch  inclined 

planes  on  the  Plane-Dropper. 

Abscissae :  =  Angles  of  inclination  (a)  of  plane  to  horizon. 
Ordinates :  =  Velocities  in  meters  per  second  and  feet  per  second. 


40  EXPERIMENTS    IN    AERODYNAMICS. 

inaccuracies  of  observation.  The  general  result  presented  by  both  the  falling 
and  soaring  planes  is  that  when  the  double  pairs  of  planes  are  placed  4  inches 
apart,  or  more,  they  do  not  interfere  with  each  other,  and  the  sustaining  power 
is,  therefore,  sensibly  double  that  of  the  single  pair  of  planes;  but  when  placed 
2  inches  apart,  there  is  a  very  perceptible  diminution  of  sustaining  power  shown 
in  the  higher  velocity  required  for  support  and  in  the  greater  rapidity  of  fall. 
Manifestly,  however,  this  result  can  hold  good  only  above  some  minimum 
velocity  of  translation,  and,  in  general,  we  may  say  that  the  closeness  with 
which  the  planes  can  be  set  without  producing  any  diminution  of  sustaining 
efficiency  is  a  function  of  the  velocity  of  translation,  so  that  the  higher  the  velocity, 
the  greater  the  proximity.  It  was  desired,  therefore,  to  ascertain  the  minimum 
velocity  for  which  the  preceding  conclusion  holds  good,  namely,  that  planes  4 
inches  wide  do  not  suffer  any  loss  of  sustaining  power  if  placed  one  above  the 
other  and  4  inches  apart.  Experiments  with  these  double  pairs  of  planes  were, 
therefore,  continued  on  August  22,  23,  and  24  for  the  purpose  of  getting  these 
data.  The  same  planes  were  used  and  were  placed  at  the  same  distance  apart, 
viz.,  2,  4,  and  6  inches,  and  a  set  of  experiments  was  also  made  with  the  single 
pair.  Previous  to  these  experiments  at  high  speeds  the  Plane-Dropper  was 
stiffened  in  order  better  to  preserve  its  vertically  under  strong  wind  pressures, 
and  precaution  was  taken  to  observe  how  closely  this  condition  was  maintained. 
The  new  observations  were  somewhat  different  from  the  early  ones,  and  consisted 
in  measuring  the  time  of  fall  of  the  double  planes — i.  e.,  one  over  the  other  when 
set  at  different  angles  ranging  from  —  7°  to  +  7°  at  three  different  velocities,  viz., 
23.6,  13.0,  and  6.5  meters  per  second.  For  every  setting  the  brass  frame  was 
turned  on  its  pivot  through  an  angle  of  180°,  so  as  to  present  first  one  side  then 
the  opposite  as  the  advancing  face.  The  two  positions  are  designated  by  A  and 
B  in  the  accompanying  Tables,  IX,  X,  and  XI,  which  contain  125  separate 
observations  at  the  above-named  different  velocities,  angles,  and  settings. 


THE    PLANE-DROPPER. 


41 


Experiments  to  determine  the  time  of  falling  of  two  sets  of  planes,  one  above  the  other  (second  series). 

TABLE  IX.— AUGUST  22, 1889. 

F.  W.  VERY,  Conducting  experiments. 

Barometer,  731.8  mm.;  mean  temperature,  23°.9  C. ;  wind,  light. 


Dimensions  and  aspect  of 
planes. 

.1 
•ft 

'm 

A 

1 

o> 
C 

Time  of  one  revo- 
lution of  turn- 
table (seconds). 

.3^8 
O  -"S  on 

w 

S 

CO 

'o  o 

9 

B 
EH 

Remarks. 

A 

0° 

0.0 

0.69 

NI|  —  ~  —  3nt  —  ~  —  !•* 

B 

0 

0.0 

0.62 

13          1         IS 

A 

0 

2.60 

23.7 

1.68 

B 

0 

2.65 

23.3 

1.70 

15  x  4  inches  (38.1  x  10.2 

B 

0 

2.60 

23.7 

1.70 

cm.). 

B 

—  2 

2.65 

23.3 

0.70 

Double   pair  of  planes.  4 

B 

—  2 

2.65 

23.3 

1.00 

inches  apart. 

A 

—  5 

2.60 

23.7 

0.75 

Total  weight,  942  grammes. 

A 

-5 

2.50 

24.6 

0.50 

A 

+  1 

2.50 

24.6 

2.20 

Fell,  then  soared. 

A 

4-  1 

2.65 

23.3 

6.15 

Fell  slowly. 

B 

—  1 

2.65 

23.3 

0.90 

B 

—  1 

2.65 

23.3 

1.20 

Same  planes,  2  inches  apart. 

A 

0° 

2.35 

26.2 

1.60 

B 

0 

2.45 

25.1 

1.20 

A 

0 

2.60 

23.7 

1.90 

B 

0 

2.60 

23.7 

1.30 

A 

4-2 

2.95 

20.9 

4.15 

Soared,  then  foil. 

B 

-2 

2.75 

22.4 

0.70 

A 

+  2 

2.70 

22.8 

5.80 

Gradual  fall,  but  very  slow. 

B 

—  2 

2.65 

23.3 

0.72 

A 

4-3 

260 

23.7 

Stayed  at  top. 

1     ** 

B 

—  3 

2.65 

23.3 

0.70 

B 

—  3 

2.75 

22.4 

0.50 

Same  planes,  6  inches  apart. 

A 

0° 

3.30 

18.7 

1.70 

B 

0 

3.30 

18.7 

1.20 

A 

0 

3.35 

18.4 

1.50 

B 

0 

3.30 

18.7 

1.30 

A 

+  1 

3.00 

20.5 

14.80 

Fell  very  slowly. 

B 

—  1 

2.95 

20.9 

1.00 

A 

4-1 

3.00 

20.5 

14.20 

Fell  very  slowly. 

B 

—  1 

3.00 

20.5 

1.10 

B 

-3 

3.15 

19.6 

0.75 

B 

—  3 

3.20 

19.2 

0.75 

Result :  It  is  certain  that  any  angle  greater  than  +  1°  (with  planes  6  inches  apart)  would 
produce  soaring,  and  as  the  error  of  verticality  in  this  day's  observations  probably  does  not 
exceed  1°  during  motion,  we  may  take  about  2°  as  the  soaring  angle  for  the  speeds  used. 


42 


EXPERIMENTS    IN    AERODYNAMICS. 


TABLE  X.— AUGUST  23, 1889. 
Barometer,  732.3  mm. ;  mean  temperature,  22° .8  C. ;  wind,  light. 


sap 

t 

£s^ 

£§, 

i 

r^H 

<o 

o  3  ^ 

ra3 

c!> 

«« 

'o 

m  "^    C 

>  £ 

_ 

Dimensions  and  aspect  of 
planes. 

'o  | 

fl  lr* 

O    ^ 

G 

si 

C  o  o> 

o     as 

"—    fl 
O    O.2 

lit 

?! 

Remarks. 

Q 
fft 

OJ  '-^  X2 

.2^0 

9 

'o 

I 

Sr3   -$ 

0  "S    03 

a 

0 

PL, 

•53 

H 

w 

H 

IS        f         IS 

A 

0° 

7.80 

7.9 

0.80 

B 

0 

9.30 

6.6 

0.70 

—  35  —  T  —  35 

A 

0 

9.10 

6.8 

0.70 

B 

0 

8.45 

7.3 

0.65 

15  x  4  inches  (38.1  x  10.2 

A 

0 

4.80 

12.8 

1.08 

cm.). 

B 

0 

4.80 

12.8 

1.02 

Double  pair  of  planes,  6 
inches  apart. 

A 
B 

0 
0 

4.85 
5:00 

12.7 
12.3 

0.90 
1.20 

Total  weight,  942  grammes. 

A 
A 

+   5 
+   5 

4.95 
10.05 

12.4 
6.1 

1.55 
0.70 

B 

—  5 

9.35 

6.6 

0.60 

B 

—  5 

4.70 

13.1 

0.64 

B 

+   5 

4.75 

13.0 

2.10 

B 

+   5 

9.00 

6.8 

0.78 

A 

—  5 

8.10 

7.6 

0.69 

A 

—  5 

4.75 

13.0 

0.70 

• 

A 

+   7 

4.85 

12.7 

11.15 

A 

+   7 

8.20 

7.5 

0.90 

B 

—  7 

9.35 

6.6 

0.62 

B 

7 

4.70 

13.1 

0.58 

B 

+   7 

4.70 

13.1 

7.25 

B 

+   7 

9.10 

6.8 

0.80 

A 

-  7 

9.50 

6.5 

0.60 

A 

-  7 

4.75 

13.0 

0.57 

A 

4-  10 

465 

133 

Soars. 

A 

p  j.\y 

10 

7.90 

7.8 

1.10 

B 

10 

10.25 

6.0 

0.75 

Same  planes,  4  inches  apart. 

A 
B 

0° 
0 

11.55 
8.60 

5.3 
7.2 

0.62 
0.60 

A 

0 

4.60 

13.4 

0.95 

B 

0 

4.70 

13.1 

0.89 

B 

+   5 

10.10 

6.1 

0.69 

B 

+   5 

4.70 

13.1 

2.30 

A 

—  5 

4.70 

13.1 

0.70 

A 

-  5 

10.20 

6.0 

0.65 

A 

+    5 

7.65 

8.1 

0.63 

A 

+   5 

4.70 

13.1 

2.90 

B 

—  5 

.4.80 

12.8 

0.59 

B 

—  5 

10.50 

5.9 

0.59 

A 

+   7 

13.70 

4.5 

0.59 

A 

+   7 

4.85 

12.7 

3.07 

B 

-  7 

4.87 

12.7 

0.58 

THE   PLANK- DROPPER. 


43 


TABLE  X.— AUGUST  23.  1889— Continued. 


Dimensions  and  aspect  of 
planes. 

Position  of  falling 
piece. 

03 
'o> 

'"0.0 

43 
Q 

a 

lime  of  one  revo- 
lution of  turn- 
table (seconds) 

Horizontal  veloc- 
ity (meters  per 
second). 

i 

"sl 

Remarks. 

-7*5         4          25 

B 

-   7° 

11.70 

5.3 

0.58 

*\                 "titti"                  1** 

B 

+    1 

11.40 

5.4 

0.69 

15                      IS 

B 

+    7 

4.85 

12.7 

2.80 

15x4    inches    (38.1x10.2 

A 

-   7 

4.90 

12.6 

0.58 

cm.). 

A 

-   7 

11.40 

5.4 

0.58 

Double  pair  of  planes,  4 

A 

+  10 

8.60 

7.2 

0.80 

inches  apart. 

A 

4-  10 

470 

13.1 

Soars. 

Total  weight,  942  grammes. 

B 

+  10 

11.00 

0.60 

Same  planes,  2  inches  apart. 

A 

0° 

11.40 

5.4 

0.58 

B 

0 

11.00 

5.6 

0.56 

A 

0 

4.90 

12.6 

0.69 

B 

0 

4.80 

12.8 

0.68 

A 

+   5 

4.50 

13.7 

1.13 

A 

+   5 

10.30 

6.0 

0.60 

B 

-   5 

9.20 

6.7 

0.55 

B 

-   5 

4.80 

12.8 

0.55 

B 

+   5 

4.90 

12.6 

0.74 

B 

+    5 

9.70 

6.4 

0.60 

A 

-   5 

9.90 

6.2 

0.56 

A 

-   5 

4.95 

12.4 

0.60 

A 

+   7 

4.95 

12.4 

1.50 

A 

+    7 

11.00 

5.6 

0.50 

B 

-   7 

10.60 

5.8 

0.52 

B 

-   7 

4.80 

12.8 

0.50 

. 

B 

+   7 

4.60 

13.4 

1.30 

B 

+    7 

9.10 

6.8 

0.60 

A 

-   7 

8.75 

7.0 

0.54 

A 

-   7 

4.90 

12.6 

0.58 

A 

+  10 

4.80 

12.8 

3.45 

A 

+  10 

10.60 

5.8 

0.60 

B 

+  10 

10.20 

6.0 

0.61 

B 

+  10 

4.90 

12.6 

1.70 

A 

+  11 

4.90 

12.6 

11.30 

Falls  slowly. 

A 

+  12 

4.90 

12.6 

27.50 

Falls  very  slowly. 

A 

+  14 

4.95 

12.4 

27.65 

Falls  very  slowly. 

A 

+  14 

4.70 

13.1 

Soars. 

Single  pair  of  planes,  15  x  4 

A 

0° 

4.60 

13.4 

0.90 

inches  (38.1  x  10.2  cm.). 

B 

0 

4.60 

13.4 

0.99 

B 

0 

8.45 

7.3 

0.64 

A 

0 

8.40 

7.3 

0.65 

A 

+    5 

8.45 

7.3 

0.69 

A 

+   5 

5.00 

12.3 

1.37 

A 

+   7 

5.00 

12.3 

2.50 

A 

+   7 

8.40 

7.3 

0.68 

A 

+  10 

7.90 

7.8 

0.79 

[soar. 

A 

+  10 

5.00 

12.3 

11.20 

Falls  slowly,  but  does  not 

44 


EXPERIMENTS    IN    AERODYNAMICS. 


TABLE  XI.— AUGUST  24,  1889. 
Barometer,  734.3  mm. ;  mean  temperature,  25°.0  C. ;  wind,  light. 


1 

A 

i 

Ml 

i  fe 

i 

3 

"3 

to*"    ° 

>  2 

_   . 

Dimensions  and  aspect  of 
planes. 

It 

ci 
o  o 

'.£ 

a  *"  ° 

lit 

t4-t     C 

0   0 

Remarks. 

•| 

"f 

III 

N            g 

• 

a 

(2 

< 

H 

B 

B 

Single  pair  of  planes,  15  x  4 
inches. 

A 
B 

—  5° 
+   5 

9.50 
9.50 

6.5 
6.5 

0.60 
0.65 

B 

+   5 

5.00 

12.3 

1.30 

IS         f         IS 

A 

—  5 

4.95 

12.4 

0.60 

A 

7 

4.85 

12.7 

0.50 

IS          i          25 

A 

—  7 

8.65 

7.1 

0.60 

B 

+   7 

9.40 

6.6 

0.70 

B 

+  10 

8.75 

7.0 

0.70 

B 

+  10 

4.95 

12.4 

1.85 

B 

+  12 

5.00 

12.3 

2.70 

B 

+  14 

5.10 

12.1 

1.60 

B 

+  14 

4.50 

13.7 

A 

0 

2.63 

23.4 

2.60 

B 

0 

2.64 

23.3 

1.07 

A 

0 

2.60 

23.7 

1.80 

B 

0 

2.60 

23.7 

1.00 

A 

-L.   i 

2.60 

237 

l^cll  after  soarin(r  about  20 

B 

i^    •* 
i 

2.65 

23.3 

1.00 

seconds. 

B 

+   1 

2.60 

23.7 

4.30 

A 

—  1 

2.58 

23.9 

1.10 

A 

—  5 

2.60 

23.7 

0.70 

' 

B 

—  5 

2.60 

23.7 

0.60 

The  actual  velocities  obtaining  in  the  individual  observations  varied  some- 
what ;  for  the  lowest  velocity  ranging  between  5  and  8 ;  for  the  second  velocity 
ranging  between  12.5  and  13.5,  and  for  the  highest  velocity  ranging  in  gen- 
eral between  22.5  and  24.0,  except  for  the  planes  6  inches  apart,  for  which  the 
velocities  were  about  19  meters  per  second.  The  numerical  results  for  the 
lowest  and  the  highest  speed  will  be  found  plotted  in  Figs.  6  and  7,  respectively. 
In  these  diagrams  the  abscissae  are  angles  of  inclination  of  the  planes  to  the 
horizon,  and  the  ordinates  are  times  of  falling.  For  the  highest  velocity,  the 
times  of  falling  of  the  single  pair  of  planes  and  of  the  double  pair,  both,  4  inches 
and  6  inches  apart,  are  alike,  while  for  the  planes  2  inches  apart,  the  time  of  falling 
is  shorter.  For  the  lowest  velocity,  viz.,  6.5  meters  per  second,  the  planes  4  inches 
apart  as  well  as  those  2  inches  apart  fall  a  little  faster  than  the  single  plane, 
and  are  therefore  not  quite  so  well  sustained  by  the  air. 

This  result  confirms  the  statement  above  made,  that  for  double  sets  of  planes, 
one  above  the  other,  the  maximum  supporting  effect  relatively  to  the  single 


THE    PLANE-DROPPER. 


45 


planes  is  obtained  only  above  a  certain  minimum  velocity  of  translation.  For 
the  present  planes,  of  size  15  x  4  inches  set  4  inches  apart,  this  minimum  velocity 
is  shown  by  the  curves  to  be  higher  than  6.5  and  less  than  23.5  meters  per 
second,  and,  from  comparison  of  all  the  data,  apparently  lies  at  about  13  meters 
per  second.  These  results  substantially  confirm  those  obtained  from  the  experi- 
ments of  June  14,  with  this  additional  information  as  to  the  minimum  velocity 
at  which  the  maximum  sustaining  power  can  be  obtained  for  a  distance  apart 
of  4  inches.  For  a  distance  of  2  inches  apart  even  the  highest  velocities  show  a 
serious  diminution  of  efficiency. 

The  results  of  these  observations  with  two  sets  of  planes,  one  above  the 
other,  give  us  a  first  conception  of  the  form  and  initial  vertical  amplitude  of  the 
wave  that  is  set  in  motion  in  the  air  by  a  plane  passing  horizontally  through  it 
in  the  manner  of  these  planes. 

FIG.  6. 


1.25 


1.00 


0.75 


0.50 


A. 
B. 


D. 


— i- 


Single  pt  irofplana 
Dandle    • 


f  Ztn  apart. 
1*- — 


C 

B 


Times  of  falling  4  feet  of  single  and  double  pairs  of  15  x  4  inch  planes  set  at  different  angles  of 

elevation  and  having  a  horizontal  velocity  of  6.5  meters  per  second. 
Abscissae :  =  Angles  of  inclination  of  plane  to  horizon. 
Ordinates :  =  Time  of  fall  in  seconds. 

These  later  observations  also  incidentally  furnish  additional  data  as  to  the 
velocity  of  soaring.  When  inclined  at  an  angle  of  10°  the  single  planes  and 
the  double  planes,  at  a  distance  of  4  inches  apart  and  upward,  are  sustained  in 
the  air  if  they  have  a  horizontal  velocity  of  about  13.2  meters  per  second. 
When  set  at  1°,  soaring  took  place  at  velocities  from  21  to  23  meters  per  second. 
Close  observation  also  indicated  that  the  error  of  verticality  of  the  plane-dropper 
during  motion  did  not  exceed  1° ;  hence  for  these  velocities  the  soaring  angle 
may  be  taken  at  about  2°.  This  is  a  fraction  of  a  degree  less  than  that  given  by 
the  observations  of  June  14,  as  plotted  on  Fig  3. 

The  most  general  and  perhaps  the  most  important  conclusion  to  be  drawn  from 
them  appears  to  be  that  the  air  is  sensibly  disturbed  under  the  advancing  piano 


46 


EXPERIMENTS    IN    AERODYNAMICS. 

FIG.  7. 


TT4T 


Times  of  falling  4  feet  of  single  and  double  pairs  of  15  x  4  inch  planes  set  at  different  angles  of 

elevation  and  having  a  horizontal  velocity  of  23.5  meters  per  second. 
Abscissae :  =  Angles  of  inclination  (a)  of  plane  to  horizon. 
Ordinates :  =  Time  of  fall  in  seconds. 


THE   PLANE-DROPPER.  47 

for  only  a  very  slight  depth  ;  so  that  for  the  planes  4  inches  apart,  at  the  average 
speeds,  the  stratum  of  air  disturbed  during  its  passage  over  it,  is,  at  any  rate,  less 
than  4  inches  thick.  In  other  words,  the  plane  is  sustained  by  the  compression 
and  elasticity  of  an  air  layer  not  deeper  than  this,  which  we  may  treat,  for  all  our 
pi'esent  purposes,  as  resting  on  a  solid  support  less  than  four  inches  below  the 
plane.  (The  reader  is  again  reminded  that  this  sustenance  is  also  partly  due  to 
the  action  of  the  air  above  the  plane.) 

Summing  up  the  results  obtained  with  the  plane-dropper,  we  have  determined : 

1.  The  relative  times  of  falling  a  distance  of  4  feet  (lm.22)  that  obtain  for 
differently  shaped  but  horizontally  disposed  planes  moving  with  different  hori- 
zontal velocities,  showing  quantitatively  the  primary  fact  that  the  time  of  fall  is 
an  increasing  function  of  the  velocity  of  lateral  movement. 

2.  The  varying  velocities  of  translation  at  which  planes  of  given  size  and 
weight,  but  of  different  shapes,  will  be  sustained  by  the  air  when  inclined  at 
different  angles. 

3.  The  maximum  proximity  at  which  successive  planes  can  be  oet  one  above 
the  other  in  order  to  give  a  supporting  power  proportional  to  their  surface. 

4.  A  first  approximation  to  the  initial  amplitude  of  the  wave  motion  origi- 
nated by  a  plane  passing  horizontally  or  at  a  small  angle  through  the  air  with  a 
considerable  velocity. 

5.  The  approximate  resistance  to  advance  of  a  wind-plane  at  soaring  speeds, 
and  (by  computation)  the  work  necessary  to  be  expended  in  overcoming  this 
resistance. 

These  experimentally  show  that  the  higher  horizontal  speeds  are  maintained 
with  less  expenditure  of  power  than  lower  ones,  and  the  quantitative  experiments 
by  which  these  results  are  established  ai*e,  so  far  as  I  am  aware,  new,  and  I 
believe  have  a  most  immediate  bearing  on  the  solution  of  the  problem  of  artificial 
flight. 

I  may  add  that  these  experiments  with  the  horizontal  plane,  when  properly 
executed,  give  results  of  a  character  to  forcibly  impress  the  spectator ;  for,  since 
there  is  no  inclination,  there  is  no  visible  component  of  pressure  to  prolong  the 
fall,  yet  the  plane  nevertheless  visibly  behaves  as  if  nearly  deprived  of  its  weight. 
The  pair  of  18  x  4  inch  planes,  for  instance,  fa  of  an  inch  thick  and  weighing 
464  grammes,  has  a  specific  gravity  of  about  1,660  times  that  of  air  ;  yet  while  the 
retardation  due  to  the  still  air  in  the  direct  fall  is  but  Os.03,  that  due  to  the  same 
air  in  strictly  lateral  motion  is  1".50 — a  most  noteworthy  result  in  its  bearing  on 
the  use  in  mechanical  flight  that  may  be  derived  from  a  property  of  the  air  much 
utilized  by  nature,  but  hitherto  almost  wholly  neglected  in  this  connection  by 
man — its  inertia. 


CHAPTER  VI. 

THE  COMPONENT  PRESSURE  RECORDER. 

The  experiments  with  the  Plane-Dropper  in  the  preceding  chapter  give  the 
soaring  speeds  of  wind-planes  of  different  shapes  set  at  varying  angles,  and  enable 
us  by  the  use  of  a  fundamental  formula  of  mechanics  to  make  a  provisional  com- 
putation of  the  work  expended  per  minute  in  their  uniform  horizontal  flight, 
neglecting  frictional  resistances. 

Among  several  conclusions,  one  of  prime  importance,  namely,  that  in  such 
aerial  motion  of  heavy  inclined  planes  the  higher  speeds  are  maintained  with  less 
expenditure  of  power  than  the  lower  ones,  presents  an  appearance  so  paradoxical 
that,  in  view  of  its  obviously  extraordinary  importance,  I  have  endeavored  to 
establish  it  independently  wholly  by  experiment,  without  the  use  of  any  formula 
whatever.  For  this  purpose  it  is  desirable  to  measure  by  means  of  a  suitable 
dynamometer  the  number  of  foot-pounds  of  work  done  in  overcoming  the  resist- 
ance to  advance  when  a  wind-plane  is  driven  at  soaring  speeds  (i.  e.,  speeds  at 
which  it  maintains  a  horizontal  course  by  virtue  of  the  vertical  component  of 
pressure,  which  in  this  case  is  just  equal  to  the  weight),  by  means  of  the  whirling- 
table,  yet  under  conditions  strictly  assimilable  to  those  of  free  flight,  in  the  case 
of  an  actual  aerodrome  propelled  by  its  own  motor. 

After  much  study  and  much  experiment,  I  gradually  perfected  an  instru 
ment  (that  described  here  as  the  Component  Pressure  Recorder),  to  be  used  in 
connection  with  the  Dynamometer-Chronograph  in  recording  the  speed,  the  resist- 
ance to  forward  motion  at  the  instant  of  soaring,  and  other  attendant  phenomena. 
Its  use  in  connection  with  the  Dynamometer- Chronograph  will  also  be  further 
described  in  chapter  VII. 

In  the  present  chapter,  I  shall  not  consider  further  the  action  of  the  self- 
propelling  model,  but  treat  of  it  as  reduced  to  its  simplest  type  of  an  inclined 
plane,  the  "  wind-plane,"  or  system  of  planes  driven  forward  by  the  turn-table 
arm  until  they  are  raised  from  it  by  the  wind  of  rotation  and  soar.  The  imme- 
diate objects  of  experiment  are,  therefore,  to  determine  soai'ing  speeds  and  the 
horizontal  resistances  corresponding  thereto. 

DESCRIPTION. 

The  Component  Pressure  Recorder  (or  Component  Recorder),  plate  VII,  may 
be  compared  to  a  balance  which  rocks  on  a  knife-edge  bearing,  in  the  ordinary 
way,  but  which  also  oscillates  horizontally  about  a  vertical  axis.  With  respect 

(48) 


THE   COMPONENT    PRESSURE    RECORDER.  49 

to  its  vertical  oscillations  about  the  knife-edge  bearing,  it  is  a  true  balance,  whose 
arms,  each  one  meter  long,  are  in  delicate  equilibrium-  an~d*I  will  call  this  part 
of  the  instrument  distinctively  "  the  balance." 

If  an  actual  working  aerodrome  model  with  its  motor  be  not  used  upon 
the  outer  arm  (outer,  that  is,  as  reckoned  from  the  center  of  the  turn-table),  a 
plane  of  given  weight  (the  "wind-plane")  is  clamped  there,  so  as  to  make  any 
desired  angle  of  inclination  with  the  horizon.  The  horizontal  oscillation  about 
the  vertical  axis  provides  for  the  measurement  of  the  horizontal  component  of 
pressure  on  this  plane ;  the  vertical  oscillation  on  the  knife-edge  provides  for 
measuring  the  vertical  component.  The  horizontal  pressure  is  measured  by  the 
extension  of  a  spring  fastened  to  an  arm  moving  around  the  axis  with  the 
horizontal  oscillation  of  the  balance,  and  to  the  surrounding  fixed  frame.  The 
vertical  component  of  pressure  is  measured  only  when  it  is  equal  to  the  weight 
of  the  plane — i.  e.,  by  the  fact  that  the  plane  is  actually  just  lifted  by  the  wind 
of  rotation,  or,  in  the  technical  term  previously  used,  when  it  soars.  The  requisite 
registration  of  this  fact  is  automatically  accomplished  by  making  an  electric 
contact.  As  the  wind-plane  is  raised,  the  inner  end  of  the  balance  descends,  until 
it  strikes  a  stop  through  which  electric  connection  is  established,  and  the 
"  making  "  of  the  current  is  registered  on  the  stationary  chronograph,  which 
at  the  same  time  records  the  speed  of  the  whirling  table  four  times  in  each 
revolution,  and  thus  the  horizontal  velocity  which  produces  a  vertical  pressure 
sufficient  to  lift  or  sustain  the  wind-plane  is  determined. 

The  detailed  manner  in  which  these  objects  are  attained  by  the  apparatus 
is  described  later  in  the  text,  and  is  shown  by  the  drawings  of  plate  VII.  The 
letters  S  designate  the  iron  supports  by  means  of  which  the  frame  of  the  recorder 
rests  upon  the  arm  of  the  whirling  table  in  such  a  manner  that  the  instrument 
is  half  above  and  half  below  it.  The  knife-edge  and  the  wind-plane  are  brought 
thereby  into  the  plane  of  rotation,  and  equal  surfaces  above  and  below  the 
supporting  arm  of  the  whirling  table  are  exposed  to  the  wind  pressure. 

The  details  of  the  knife-edge  bearings  are  shown  on  the  plate  in  enlarged 
scale.  It  is  evident  that  when  the  balance  resting  on  its  knife-edge  is  in  motion 
on  the  whirling  table,  there  will  be  an  outward  thrust  on  the  instrument  tending 
to  throw  the  knife-edge  off  from  its  bearing.  In  order  to  take  up  this  thrust, 
and  yet  in  no  way  impair  the  action  of  that  portion  of  the  instrument  which 
acts  the  part  of  a  balance,  a  pair  of  cylindrical  pivots  exactly  concentric  with  the 
prolongation  of  the  knife-edge  are  made  to  extend  out  beyond  the  knife-blade 
arid  rest  in  a  suitable  bearing.  The  pivots  thus  arranged  take  up  the  outward 
thrust  arising  from  centrifugal  force,  while  the  freedom  of  motion  of  the  balance 
vja  the  knife-edge  is  not  at  all  impaired. 

7 


50  EXPERIMENTS    IN    AERODYNAMICS. 

The  wind-plane  is  fastened  to  a  brass  tube  on  the  outer  end  of  the  instrument, 
and  set  to  any  angle  of  inclination  by  means  of  the  graduated  circle  G.  This 
tube  is  adjustable  in  position  so  that  the  center  of  the  wind-plane,  whatever  be 
its  size,  is  at  a  constant  distance  of  1.25  meters  from  the  center  of  the  balance 
and  of  the  whole  instrument.  A  similar  adjustable  tube  on  the  inner  arm 
serves  to  adjust  the  balance  to  equipoise  for  any  position  of  the  outer  tube. 
Beneath  the  inner  arm  of  the  balance  a  registering  arm  is  rigidly  fastened  to 
the  vertical  axis,  and  partakes  of  the  horizontal  oscillation  of  the  balance,  but 
not  of  its  vertical  motion.  Near  its  extremity  is  attached  the  horizontal  spring 
already  referred  to,  and  at  the  end  it  carries  a  pencil,  which  registers  on  a 
revolving  chronograph  cylinder  below  the  extension  of  the  spring  produced  by 
the  horizontal  pressure  on  the  wind-plane. 

The  length  of  the  record  arm  from  center  of  balance  to  spring  is  28.5  inches, 
(72.4  cm.) 

The  length  of  the  record  arm  from  center  of  balance  to  pencil  is  31.5  inches, 
(80.0  cm.) 

The  pencil  departures  are  therefore  longer  than  the  true  spring  extension, 
and  the  latter  are  obtained  from  the  former  by  multiplying  by  the  factor 

|f|  =  0.905. 
ol.o 

To  reduce  the  pull  on  the  spring  to  what  it  would  be  if  the  spring  had  the 
same  lever  arm  as  the  center  of  the  plane,  we  must  multiply  it  by  the  factor 

72  4 

expressing  the  ratio  of  the  lengths  of  the  arms,  viz.,  ,     '     =  0.579. 

125.0 

Within  the  limits  of  attainable  precision,  we  observe  the  spring  calibration 
to  be  linear,  and  the  two  factors  may  be  multiplied  together,  giving  the  single 
factor  0.524,  by  which  the  pressure  corresponding  to  pencil  departures,  as  taken 
from  the  calibration  curves,  must  be  multiplied  in  order  to  get  the  pressures  on 
the  plane.  The  horizontal  springs  used  in  these  experiments  are  those  hereafter 
more  fully  described  in  connection  with  the  Rolling  Carriage. 

The  uniform  distance  from  the  center  of  rotation  of  the  turn-table  to  the 
center  of  wind  plane  is  9.55  meters.  The  balance  arms  are  protected  from  wind 
by  covering  the  sides  of  the  surrounding  frame  with  cloth  and  paper  and  placing 
over  the  top  an  adjustable  lid  of  veneer.  An  experimental  test  of  the  Recorder 
without  wind-plane  was  first  made,  to  discover  the  effect  of  any  residual  wind 
pressure  on  the  arms.  The  instrument  was  carefully  adjusted  on  the  turn-table, 
and  then  set  in  rapid,  uniform  motion  without  exhibiting  any  tension  of  the 
horizontal  spring.  The  result  indicates  that  whatever  wind  pressure  still 
remains  is  equal  on  both  arms.  It  is  to  be  noted  that  a  theoretically  perfect 
measurement  of  horizontal  wind  pressure  by  this  instrument  requires  a  uniform 


THE   COMPONENT    PRESSURE    RECORDER.  51 

velocity  of  the  turn-table  at  the  instant  for  which  the  reading  is  made.  The 
occasion  for  this  condition  arises  in  the  circumstance  that  with  a  varying 
velocity  the  inertia  of  the  inner  arm  of  the  balance  produces  a  different  effect  on 
the  instrument  from  the  inertia  of  the  outer  arm  ;  thus  with  increasing  velocities 
the  outer  arm  tends  to  go  slower  than  the  inner  arm,  and  with  decreasing  veloci- 
ties tends  to  go  faster.  This  differential  effect  of  inertia  is  taken  up  by  the  spring 
and  is  combined  with  the  wind  pressure  until  a  uniform  velocity  is  attained,  and 
then  the  wind  pressure  alone  remains  to  extend  the  spring. 

Each  arm  of  the  balance  carries  a  brass  friction  wheel,  R,  which  is  intended 
to  rest  upon  a  track,  P  P',  thereby  limiting  the  vertical  motion  of  the  balance 
arms.  When  the  wind-plane  is  vertical,  and  horizontal  wind  pressure  is  being 
measured,  the  outer  arm  carrying  the  plane  rests  continuously  on  the  track  and 
the  friction  wheel  affords  perfect  freedom  of  horizontal  motion  of  the  balance, 
which  fulfills  its  proper  function  at  the  same  time  that  it  turns  about  the  vertical 
axis ;  so  that  when  the  plane  is  inclined  and  is  raised  by  the  vertical  component 
of  the  wind — i.  e.,  when  the  wind-plane  soars — the  inner  arm  is  brought  down 
to  the  stop  P  and  the  friction  wheel  insures  free  motion  of  the  balance  about  the 
vertical  axis.  An  electric  wire  connects  with  P,  and  a  second  wire  carries  a 
current  through  the  knife-edges  into  the  balance,  and  thence  to  the  friction  wheel, 
where  the  electric  current  is  completed  at  the  moment  of  contact  between  the 
friction  wheel  and  the  stop.  After  leaving  the  whirling  table  the  current  passes 
through  an  electric  bell,  which  serves  to  inform  the  experimenter  of  the  fact  of 
soaring  (though  this  is  independently  recognizable  by  the  motion  of  the  arm), 
and  thence  to  the  observatory  chronograph,  where  the  contacts  are  registered. 
On  this  chronograph,  then,  are  registered  (1)  the  second-beats  of  the  mean  time 
standard  clock  of  the  observatory ;  (2)  the  contacts,  which  are  made  four  times 
in  every  revolution  of  the  turn-table  and  show  its  speed,  and  (3)  the  electric 
current  which  registers  soaring ;  the  two  latter  records  being  clearly  distin- 
guishable. 

The  actual  method  of  experiment  employed  to  determine  the  velocity  at 
which  soaring  is  just  attained  is  as  follows:  The  velocity  of  the  whirling  table 
is  increased  to  the  point  at  which  soaring  almost  begins  to  take  place — that  is, 
when  the  plane  begins  to  flutter.  This  velocity  is  then  still  further,  but  very 
slowly,  increased  and  adjusted  until  the  electric  bell  rings  as  nearly  as  possible 
half  the  time.  The  velocity  at  which  this  occurs  represents  that  of  soaring. 
This  method  is  based  on  the  following  considerations :  If  the  precise  velocity  be 
attained  at  which  the  plane  would  be  just  sustained  in  quiet  air,  not  resting  on 
the  stop  at  either  end,  the  actual  wind  which  prevails  to  a  greater  or  less  extent 
in  the  open  air  disturbs  this  equilibrium  and  causes  the  plane  to  be  more  than 
sustained  during  the  half  revolution  of  the  turn-table  which  carries  it  against 


52 


EXPERIMENTS    IN   AERODYNAMICS. 


the  wind,  and  less  than  sustained  during  the  remaining  half.  Consequently, 
this  condition  of  electric  contact  half  the  time  is  taken  to  be  the  one  desired,  and 
the  velocity  corresponding  to  it  is  taken  from  the  chronograph  and  called  the 
soaring  velocity  for  the  plane  and  angle  obtaining  in  the  experiment.  When 
the  electric  bell  indicates  to  the  observer  an  exact  soaring,  the  speed  is  main- 
tained uniformly  for  a  few  revolutions,  as  required  by  the  theory  of  the  Recorder 
already  alluded  to,  as  a  requisite  for  the  proper  measurement  of  the  wind  pressure 
on  the  plane.  A  brush  H  is  attached  to  the  inner  arm  of  the  balance  for  the 
purpose  of  producing  a  regulated  friction,  and  thereby  diminishing  somewhat 
the  fluctuations  of  the  apparatus,  which  was  found  to  be  too  sensitive  to  currents 
to  do  work  of  all  the  accuracy  it  is  capable  of,  except  in  calm  weather. 

Some  preliminary  experiments  were  made  in  August,  1889,  to  determine  the 
relative  velocities  of  soaring  of  different  planes.  But  the  first  Component- Recorder 
was  shortly  afterwards  destroyed  in  an  accident,  and  the  observations  were  inter- 
rupted until  September,  1890,  when  they  were  resumed  with  the  newly  constructed 
and  improved  Component- Recorder  figured  in  the  plate.  Nine  new  planes  were 
made  of  light  pine,  and  backed  with  lead  so  as  to  have  the  following  sizes  and 
weights : 


i 

5ize. 

Weight.    [ 

E 

Size. 

Weight. 

E 

dze. 

Weight. 

Inches. 

Cm. 

Grammes.  : 

Inches. 

Cm. 

Grammes. 

Inches. 

Cm. 

Grammes. 

30  x  4.8 
SO  x  4.8 
30x4.8 

76.2  x  12.2 
76.2  x  12.2 
76.2  x  12.2 

250 
500 
1,000 

24x6 
24x6 
24x6 

61.0  x  15.2 
61.0x15.2 
61.0  x  15.2 

250 
500 
1,000 

12x12 
12x12 
12x12 

30.5  x  30.5 
30.5  x  30.5 
30.5  x  30.5 

250 
500 
1,000 

It  was  found  that  the  heavier  planes,  and  especially  the  longer  ones,  required 
light  trussing  in  order  to  prevent  them  from  bending  when  in  rapid  motion. 
This  was  effected  by  inserting  a  transverse  arm  of  round  brass  in  the  end  of  the 
brass  tube  where  the  planes  are  attached,  and  carrying  fine  steel  wire  out  to  the 
extremity  of  the  plane.  The  30-inch  plane  was  further  trussed  by  a  post  at  its 
center  carrying  wires  to  the  four  corners. 

Inasmuch  as  the  center  of  pressure  on  an  inclined  plane  is  in  front  of  the 
center  of  figure  (as  will  be  shown  in  connection  with  the  Counterpoised  Eccentric 
Plane),  the  lead  backing  was  inserted  to  one  side  of  the  center,  so  as  to  bring  the 
center  of  gravity  into  approximate  coincidence  with  the  center  of  pressure  when 
the  plane  is  inclined  at  low  angles,  and  the  plane  was  grasped  at  a  similar 
distance  in  front  of  the  center.  These  provisions  contributed  to  diminish  the 
twisting  of  the  planes.  These  planes  were  used  until  November  25,  when  they 


THE    COMPONENT    PRESSURE    RECORDER. 


53 


were  replaced  by  others  backed  with  strips  of  brass,  which  gave  the  planes  the 
desired  weight,  and  also  contributed  the  necessary  stiffness.  The  latter  planes 
are  made  of  pine  t  of  an  inch  thick,  with  square-cut  edges.  The  brass  strip 
is  a  piece  of  hard-rolled  brass  running  the  whole  length  of  the  plane,  and  about 
2  inches  wide.  In  the  24  and  30  inch  planes  the  middle  of  the  strips  was  bent 
slightly  outward — i.  e.,  "  corrugated  " — for  greater  stiffness. 

The  experiments  were  made  in  two  series.  The  first  series  was  made  on 
eight  days,  from  September  29  to  October  9,  inclusive,  and  consisted  in  deter- 
mining the  soaring  speeds  and  corresponding  resistances  of  the  above-described 
planes  set  at  angles  from  2°  to  30°,  and  the  horizontal  pressure  on  the  planes 
when  set  at  90° — that  is,  normal  to  the  line  of  advance.  In  all,  95  complete 
observations  were  taken. 

The  following  is  an  example  of  the  original  record  made  in  these  observa- 
tions, extracted  from  the  note  book  for  October  8  : 

Experiments  with  Component  Pressure  Recorder  to  determine  horizontal  pressures  at  soaring  speeds. 

OCTOBER  8,  1890. 
F.  W.  VERY,  Conducting  experiments ;  JOSEPH  LUDEWIG,  Regulating  engine. 

Barometer,  736.6;  temperature,  15°  C. ;   air  meter  at  10:30  a.  m.,  1,509,500;   air  meter  at 
3:20  p.  m.,  1,500,400;  30  x  4.8  inch  plane;  weight,  500  grammes;  spring  No.  2. 


Angle. 

Seconds  in  one  revo- 
lution of  turn-table. 

Velocity  of  plane 
(meters  per  sec- 
ond). 

Extension  of  spring 
(inches).* 

Pull  of  spring 
(grammes). 

90° 

12.10 
10.05 
9.60 

4.96 
5.97 
6.25 

1.40 
2.20 
2.45 

45 
472 
526 

*The  use  of  an  English  scale  instead  of  a  metric  one  in  measuring  the  spring  extensions  introduces  a  lack 
of  harmony  in  the  system  of  units  employed  that  is  not  to  be  recommended ;  but  since  this  is  a  record  of  the 
original  observations,  the  measurements  as  actually  made  are  faithfully  presented. 


54 


EXPERIMENTS    IN    AERODYNAMICS. 


Angle. 

Seconds  in  one  revo- 
lution of  turn-table. 

Estimated   soaring 
speed  (meters  per 
second). 

Spring 
extension 
(inches). 

Remarks. 

30° 

5.5   >      1 

6.3    < 

5.5   >       }•  5.65  sees. 

10.6 

2.3 

5.75  < 

5.55  >      J 

15° 

4.8   »^ 

5.4   > 

5.65  right 
6.3    « 
5.9    < 

•  5.75 

10.4 

0.8 

Plane  quivers  at  tip  with 
highest  speed. 

5.85  right  , 

10° 

5.0  >      ' 

5.4   right 

5.85  < 

K    C           jf 

•  5.35 

17.9 

0.75 

Plane  somewhat  bowed. 

5.5    < 

5.3    < 

5.3   right. 

Plane  stiffened  by  thin  iron  plate  at  both  ends  and  at  middle,  and  experiment 

repeated  with  same  setting. 

10° 

4.9   >      1 

5.0    < 

(Repeated) 

4.75  >       U.95 
5.1    < 

12.1 

0.9 

5.0   <      J 

The  extensions  of  the  spring  corresponding  to  the  horizontal  component  of  pressure 
on  the  plane,  and  caused  by  the  movement  of  the  Recorder  about  the  vertical 
axis,  are  taken  from  the  sheet  of  the  recording  cylinder  carried  on  the  turn-table 
arm,  as  already  described  and  as  shown  on  plate  7.  The  records  of  velocities 
are  found  on  the  stationary  chronograph  registering  the  quadrant  contacts  of 
the  turn-table,  and  on  the  same  sheet  with  the  electric  contacts  made  at  soaring 
speeds.  Thus,  when  the  latter  sheet  has  been  taken  off  its  chronograph  barrel, 
the  observer  has  before  him  a  permanent  record  of  the  velocity  of  the  turn-table 
measured  four  times  in  every  revolution,  and  together  with  it  the  trace  of  the 
irregular  contacts  made  by  the  vertical  rocking  of  the  balance  arm  which  takes 
place  at  soaring  speed.  Now,  since  the  criterion  of  exact  soaring  is  that  these 
signals  shall  appear  on  the  trace  half  the  time  of  each  revolution,  an  inequality 
mark  is  added  to  the  record  of  the  measured  velocities,  which  indicates  how 
nearly  this  condition  is  attained.  If  the  chronograph  sheet  for  any  complete 
revolution  of  the  turn-table  is  more  than  half  filled  with  the  signals,  the  velocity 


THE   COMPONENT    PRESSURE    RECORDER. 


55 


is  too  great ;  if  less  than  half  filled,  the  velocity  is  too  small,  etc.  Two  or  more 
inequality  marks  are  used  to  indicate  a  wide  difference  from  the  mean  condition. 
By  putting  down  a  series  of  such  readings  measured  at  a  number  of  revolutions 
of  the  turn-table  and  taking  a  mean  estimate,  a  very  close  approximation  to  the 
soaring  speed  may  be  made,  and  the  result  has  the  weight  of  a  very  considerable 
number  of  single  readings. 

After  completing  the  experiments  of  September  29  to  October  9  according 
to  the  plan  laid  out,  the  observations  were  reduced,  and  their  discussion  served 
to  show  that  additional  experiments  were  needed  to  supplement  them.  There- 
upon a  second  series  was  instituted  for  the  purpose  of  obtaining  additional  data. 
In  this  series  the  following  five  planes  were  used  : 


Size. 

Weight. 

(Inches.) 

(Centimeters.) 

(Grammes.) 

30  x    4.8 

76.2  x  12.2 

500 

24  x    6 

61.0  x  15.2 

500 

12x12 

30.5  x  30.5 

500 

12  x    6 

30.5  x  15.2 

250 

6x    6 

15.2  x  15.2 

125 

The  principal  further  objects  to  be  attained  were  to  determine  with  greater 
precision  the  soaring  speeds  of  the  24  x  6  and  30  x  4.8  inch  planes  at  small  angles 
and  the  horizontal  pressure  at  those  speeds  ;  to  determine  the  soaring  speed  for 
angles  of  the  plane  above  30°,  so  as  to  get  the  minimum  point  in  the  soaring 
speed  curve — that  is,  to  determine  the  angle  at  which  soaring  takes  place  with 
minimum  velocity ;  and  to  ascertain  the  effect  of  size  of  plane  on  soaring  speed 
by  adding  to  the  planes  previously  used  two  of  smaller  size,  viz.,  12  x  6  inches 
and  6x6  inches,  having  a  corresponding  diminution  of  weight.  The  five  planes, 
therefore,  all  have  sizes  and  weights  in  the  proportion  of  500  grammes  to  the 
square  foot*  (or  5,382  grammes  to  the  square  meter),  and  their  soaring  speeds  are 
entirely  comparable  for  indicating  the  relative  effect  of  shape  and  size.  The  new 
observations  were  carried  out  on  November  25,  26,  December  5  and  11,  and  com- 
prised over  80  individual  experiments.  The  detailed  observations  of  both  series 
are  presented  in  Tables  XIV  and  XV,  placed  at  the  end  of  this  chapter. 

The  column  headed  "  description  of  planes"  gives  the  dimensions  and  weight 
of  the  planes.  The  aspect  of  the  plane — i.  e.,  its  position  with  respect  to  the 

*  The  square  foot  was  adopted  as  a  unit  in  the  earliest  experiments,  and  its  use  has  been  continued  as  a 
matter  of  experimental  convenience,  owing  to  considerations  bearing  upon  the  uniformity  of  apparatus.  Were 
these  experiments  to  be  recommenced,  I  should  prefer  to  use  0.  G.  S.  (or  at  least  metric)  units  throughout. 


56  EXPERIMENTS    IN    AERODYNAMICS. 

direction  of  advance — is  indicated  by  the  order  in  which  the  dimensions  are 
stated,  the  first  dimension  being  always  the  horizontal  edge  parallel  to  the 
whirling  arm.  Thus  the  24  x  6  inch  plane  is  placed  with  its  24-inch  edge  hori- 
zontal and  parallel  to  the  whirling  arm,  and  the  6  x  24  inch  plane  is  the  same 
plane  placed  with  its  6-inch  edge  horizontal  and  parallel  to  the  whirling  arm. 
This  difference  of  position,  then,  will  be  uniformly  spoken  of  as  the  aspect  of  the 
plane.  The  column  "  pull  of  spring  "  contains  the  spring  extensions  converted 
into  pressures  by  means  of  the  calibration  curves,  and  the  column  "  horizontal 
pressure  on  plane  "  (i.  e.,  the  horizontal  component  of  pressure)  is  obtained  by 
multiplying  the  spring  pressure  by  the  factor  0.524,  which  arises  from  the  unequal 
lengths  of  the  arms  of  the  instrument.  The  next  column,  headed  "  km"  gives 
for  the  observations  with  normal  planes  the  computed  value  of  the  coefficient  in 
the  equation  P  =  km  V'2,  where  F  is  expressed  in  meters  per  second,  and  P  is  the 
pressure  on  the  plane  in  grammes  per  square  centimeter.  The  column  "  k  "  gives 
the  corresponding  value  of  this  coefficient  in  English  measures,  the  velocity  being 
expressed  in  feet  per  second  and  the  pressure  in  pounds  per  square  foot. 

SOARING  SPEEDS. 

The  soaring  speeds  determined  in  these  two  series  of  experiments  are  plotted 
in  Figs.  8  and  9,  in  which  the  abscissae  are  angles  of  inclination  of  the  planes  to 
the  horizon,  and  the  ordinates  are  the  soaring  speeds  which  correspond  to  them. 
Figure  8  contains  the  observations  made  with  the  planes  that  weigh  250  and  1,000 
grammes  to  the  square  foot,  and  Fig.  9  those  made  with  the  planes  that  weigh 
500  grammes  to  the  square  foot  (5,382  grammes  to  the  square  meter).  The 
experiments  with  the  first  two  of  these  classes  of  planes,  plotted  in  Fig.  8,  were 
not  repeated,  and  consequently  the  curves  do  not  possess  so  high  a  quantitative 
value  as  obtains  in  the  case  of  most  of  the  planes  weighing  500  grammes  to  the 
square  foot,  but  they  serve  to  present  several  fundamental  relations : 

First,  they  show  quantitatively,  when  taken  together  with  the  curves  of  Fig. 
9,  the  increase  of  velocity  necessary  to  sustain  the  heavier  planes  (per  unit  area) 
over  that  which  will  sustain  the  lighter  ones,  at  the  same  angle  of  inclination. 

Second,  the  curves  both  of  the  250  and  the  1,000  gramme  planes  show  the 
difference  due  to  shape  and  aspect,  the  soaring  speeds,  for  small  angles  of  inclina- 
tion, being  much  less  for  those  planes  whose  extension  from  front  to  back  is  small, 
than  for  those  in  which  this  dimension  is  large,  so  that,  in  general,  the  planes 
having  this  dimension  smaller,  for  small  angles  of  inclination,  soar  at  lower 
speeds.  This  result  entirely  accords  in  character  with  that  already  obtained  witli 
the  Plane- Dropper;  and,  when  freed  from  accidental  errors,  the  present  data  are 
of  higher  quantitative  value,  because  in  this  apparatus  there  are  no  guides,  and 
the  plane  has  practically  perfect  freedom. 


THE   COMPONENT    PRESSURE    RECORDER. 


57 


D 


Re/ 


(301 


•rerive 


•:h  plane 


lane,  uxiyhtft  Wgrumn  a. 


h  plane 


zon^  at.) 


'0 

horizontal.) 


weight  *.  fflgrrami.  wi 


D 


-30 


FIG.  8. 
28 

27 

26 

es 


23 
22 
21 
20 

Id 
18 
17 
18 
15 
14 
Id 
IE 
II 

10 
9 
8 
7 


A.  £4*  lindipla  le,  ivtlOt,  Oaramrn  *t. 

C  24<inch*iu  'e  horizoi  \ieil.) 


D 


}.6x&  inchpla.  te,  wllOO*  ^ yrttmrnt  t. 
korizom  at.) 


-re- 


plane, 
tide 


30*4>.8L  ich plant  weight Z,  fOpmmr. 
orizontt  I.) 


weight 
haizontjd.) 


Velocities  of  soaring  of  inclined  planes  obtained  with  the  Component  Pressure  Recorder. 
Abscissae :  =  Angles  of  inclination  («)  of  plane  to  horizon. 
Ordinates  :  =  Velocities  in  meters  per  second. 
8 


58  EXPERIMENTS    IN    AERODYNAMICS. 

Third,  many  of  the  curves  show  a  tendency  to  reach  a  minimum  point  for 
an  inclination  of  the  planes  of  about  30°,  the  highest  angle  at  which  these  planes 
were  used.  It  was,  therefore,  seen  to  be  desirable  to  extend  the  angles  of  inclina- 
tion far  enough  to  include  the  minimum  point  of  the  curve  within  the  range  of 
observation. .  This  was  done  in  the  case  of  four  of  the  planes  whose  results  are 
plotted  in  Fig.  9.  In  examining  these  curves,  it  will  be  seen  that  the  minimum 
point  falls  between  25°  and  35°.  It  should  also  be  noted  that  the  change  in  the 
soaring  speed  is  quite  small  for  settings  between  25°  and  40°,  and  that  in  a 
number  of  individual  observations  the  real  character  of  the  curve  over  this  range 
was  masked  by  the  errors  introduced  by  wind  and  weather. 

Since  the  planes  whose  results  are  plotted  in  Fig.  9  all  have  the  same 
weight  per  unit  area,  the  difference  in  their  soaring  speeds  arises  solely  from  their 
difference  of  size,  shape,  or  aspect.  The  effect  of  shape  and  aspect  indicated  in 
Fig.  8  is  beautifully  exhibited  and  amply  confirmed  in  the  six  comparable  curves 
of  Fig.  9.  For  low  angles,  viz.,  below  15°  or  20°,  the  curves  of  soaring  speed 
for  the  different  planes  occupy  the  following  relative  positions  from  below 
upward  :  30  x  4.8  inches,  24  x  6  inches,  12  x  6  inches,  6x6  and  12  x  12,  6  x  24 
inches.  It  will  be  observed  that  the  planes  placed  in  the  above  order  are 
symmetrically  arranged.  Remembering  that  the  first  written  dimension  is  the 
horizontal  edge,  perpendicular  to  the  line  of  motion,  which  may  be  called  the 
spread,  and  that  the  second  written  dimension  is  the  inclined  edge,  or  the  distance 
from  front  to  back,  it  will  be  seen  that,  in  the  above  order,  the  ratio  of  the  spread 
to  the  extent  from  front  to  back  is  uniformly  diminishing.  In  other  words,  the 
planes  whose  spread  is  largest  in  comparison  with  their  extent  from  front  to  back 
have  the  smallest  soaring  speed,  and  these  planes  are  therefore  to  be  considered 
as  being,  in  shape  and  aspect,  the  most  favorable  for  mechanical  flight.  Thus  the 
30  x  4.8  inch  and  the  24  x  6  inch  planes  are  favorable  forms  and  aspects,  while 
the  12  x  12  inch  plane  and,  to  a  greater  degree,  the  6  x  24  inch  plane  are 
unfavorable  forms  and  aspects. 

Between  15°  and  30°,  and  in  general  at  about  30°,  a  reversal  takes  place, 
and  for  higher  angles  the  curves  are  all  found  from  below  upward  in  the  reverse 
order.  Thus  the  30  x  4.8  inch  plane,  which  for  low  angles  soars  at  the  lowest 
speed,  for  settings  above  30°  requires  the  highest  speed.  This  relative  efficiency 
for  low  angles  was  manifested  in  the  experiments  with  the  Plane- Dropper,  but 
the  reversal  in  the  position  of  the  curves  for  higher  angles  is  a  relation  which 
those  observations  were  not  sufficiently  extended  to  present.  The  interpretation 
of  this  reversal  will  be  developed  by  a  consideration  of  the  general  relations 
existing  between  these  results  and  the  total  normal  pressure  on  the  planes,  and 
will  also  be  found  to  be  connected  with  corresponding  changes  in  the  relative 
positions  of  the  center  of  pressure. 


THE   COMPONENT   PRESSURE    RECORDER. 
FIG.  9. 


59 


40 


43 


50 


Velocities  of  soaring  of  inclined  planes  obtained  with  the  Component  Pressure  Recorder. 
Abscissae :  =  Angles  of  inclination  (a)  of  plane  to  horizon. 
Ordinates :  =  Velocities  in  meters  per  second. 


60  EXPERIMENTS  IN  AERODYNAMICS. 

The  pressure  on  a  plane  moving  normally  in  the  air  is  usually  represented 
by  the  equation 

p k  AT- B_ 

~l+  0.00366  (t  -  10°)  760' 

where  F  is  the  velocity  of  the  plane ;  A  is  its  area,  B  the  atmospheric  pressure 
in  millimeters,  t  the  temperature  in  centigrade  degrees,  and  k  a  coefficient  whose 
value  for  a  standard  temperature  of  10°  C.  is  determined  by  experiment.  If  the 
pressure  per  unit  area  is  different  for  planes  of  different  sizes  and  shapes,  it  will 
be  manifested  by  differences  in  the  resulting  values  of  k.  Then,  if  k  be  given 
its  value  for  a  plane  of  some  fixed  size  and  shape,  one  or  more  additional  factors 
must  be  inserted  in  order  that  the  formula  shall  give  the  pressure  on  a  plane  of 
any  other  size  and  shape.  Experiments  show  that  the  variations  in  k  for  planes 
of  different  shapes  and,  within  the  range  of  experiment,  for  planes  of  different 
sizes,  are  very  small. 

Proceeding  now  to  the  case  of  inclined  planes,  and  for  our  present  purpose 
neglecting  the  pressure  and  temperature,  we  may  represent  the  resultant  pressure 
P.  on  an  inclined  plane  moved  horizontally  in  the  air  at  an  angle  a  with  the 
horizon  by  the  equation 

l\  =  PwF(a)=kA  V*F(a), 

where  F  (a)  is  a  function  to  be  determined  by  experiment.  From  this  equation 
also  we  obtain  directly  the  vertical  component  of  pressure 

W=  Pa  cos  a  =  k  A  V2  F  (a)  cos  a 
and  the  horizontal  component  of  pressure 

R  =  P.  sin  a  =  k  A  V2  F  (a)  sin  a.  * 

The  point  to  which  I  wish  now  to  direct  especial  attention  is  that,  although  shape 
and  aspect  of  plane  have  but  slight  effect  on  the  pressure  on  normal  planes,  they 
have  a  most  important  influence  in  determining  the  pressure  on  inclined  planes. 
Consequently,  F  (a)  must  be  determined  separately  for  planes  of  different  size, 
shape,  and  aspect.  An  empirical  curve  (Fig.  1)  representing  F  (a)  for  a  square 
plane  has  been  obtained  from  the  experiments  with  the  Resultant- Recorder. 

It  is  obvious  that  the  above  equation  for  W  furnishes  the  basis  for  determin- 
ing F  (a)  for  variously  shaped  rectangles  from  the  observations  of  soaring  speed 
obtained  with  the  Component- Recorder,  together  with  experiments  on  normal 
planes.  The  vertical  component  of  pressure  at  soaring  speed  is  the  weight  of 
the  plane,  k  is  the  fundamental  constant  of  normal  pressure  derived  from 
experiments  on  the  normal  plane,  and  Fis  the  soaring  speed  for  the  angle  a. 

*Note  to  Second  Edition.  I  do  not  desire  to  multiply  formulae  where  it  can  be  avoided,  as  this  book  is 
meant  to  be  only  the  statement  of  facts  of  observation,  but  a  simple  resume  of  these  facts  in  algebraic  gener- 
ality would  take  this  form : 

F  (a)  is  of  the  form  C  sin  B  a"  where  «>  1  in  long  aspects  [    •*-   |  and  F  (a)  is  of  the  form  C  sin  B  a." 

where  »  «O  in  broad  aspects  1 4—  I,  where  C  is  a  constant  and  B  the  angle  between  the  tangent  and  the  vertical. 


THE   COMPONENT    PRESSURE    RECORDER. 


61 


For  the  12  x  12  inch  square  plane,  and  for  the  30  x  4.8  inch  and  the  6  x  24 
inch  planes,  which  last  two  are  the  planes  having  the  extremes  of  aspect,  F  (a) 
has  been  computed  from  the  above  equation  for  W,  and  the  results  are  plotted  in 
Fig.  10.  In  this  computation  W  is  500  grammes  ;  V  is  taken  from  the  soaring 
speed  curves  for  successive  values  of  a,  and  the  adopted  value  of  km,  viz.,  0.0080, 
in  metric  units,  is  the  mean  value  given  by  the  normal  planes  in  these  experi- 
ments. Comparing  the  resulting  curve  for  the  12-inch  square  plane  with  the 
curve  derived  from  the  experiments  with  the  Resultant  Pressure  Recorder,  we 
tind  the  following  values  : 

TABLE   XII. 

F  (a),  or  the  ratio  of  the  pressure  on  an  inclined  plane  one  foot  square, 
to  the  pressure  on  the  same  normal  plane. 


J 

1         K^ 

•i'O  >> 

S73^ 

Si    03  ^ 

d 

a   o  Vj 

0 

~  &  a 

^~           fl      • 

1 

8:3 

/^  V  /.R 

III? 

"u 

^  fe  & 

2  fe  &S 

Difference. 

VH 

q3-«  o 

-C'tt  a>  j, 

0 

•S 

all 

O  OH  ttt 

d  s  a  g 
1(511 

p 

(5 

s 

45 

93 

91 

+  .02 

40 

89 

88 

+  .01 

35 

84 

84 

.00 

30 

78 

78 

.00 

25 

71 

69 

+  .02 

20 

60 

57 

+  .03 

15 

46 

44 

+  .02 

10 

30 

30 

.00 

5 

15 

16 

-.01 

The  agreement  between  these  values  of  F  (a)  derived  from  these  two  entirely 
dissimilar  methods  of  observation  (dependent  also,  as  it  is,  on  the  experimental 
value  of  km)  bespeaks  the  essential  harmony  of  the  entire  system  of  results.  If, 
now,  the  curves  of  soaring  speed  have  been  determined  for  the  30  x  4.8  inch 
and  6  x  24  inch  planes  with  the  same  degree  of  accuracy  as  for  the  12-inch  square 
plane,  the  computed  values  of  F  (a)  for  these  planes  has  the  same  precision  as 
that  for  the  12-inch  square  plane. 

Looking  at  the  curves,  we  find  that  for  small  angles  the  resultant  normal 
pressure  is  greatest  in  the  30  x  4.8  inch  plane  and  least  on  the  6  x  24  inch  plane ; 
but  for  angles  above  30°  this  relation  is  reversed. 

The  reversal  in  the  relative  positions  of  the  curves  of  soaring  speed  at  an 
angle  of  inclination  of  about  30°,  for  differently  shaped  planes,  is  now  seen  to 


62 


EXPERIMENTS    IN    AERODYNAMICS. 
'    FIG.  10. 


5  10  15  20  25  30  35  40  43  50 

Ratio  of  the  resultant  normal  pressure  (Pa)  on  an  inclined  rectangle  to  the  pressure  (PK)  on 
a  normal  rectangle,  computed  from  experiments  with  the  Component  Pressure  Recorder. 
Abscissae :  =  Angles  of  inclination  (a)  of  plane  to  horizon. 

W  P 

Ordinates :  =  F(a)  =  —  _  =  ~  (expressed  as  a  percentage). 


THE   COMPONENT   PRESSURE    RECORDER.  63 

be  due  to  a  reversal  in  the  total  normal  pressure  on  the  planes.*  Thus,  shape 
and  aspect  of  plane,  while  having  but  slight  influence  in  modifying  the  pressure 
when  the  plane  itself  is  normal  to  the  wind,  are  most  important  factors  when  the 
plane  is  inclined.  This  predominating  influence  of  aspect  is,  so  far  as  I  am 
aware,  now  for  the  first  time  clearly  set  forth  with  quantitative  data.f 

HORIZONTAL  PRESSURES. 

With  every  observation  of  soaring  speed,  the  horizontal  pressure  on  the 
plane  has  been  measured  by  means  of  a  horizontal  spring.  The  detailed  obser- 
vations in  Tables  XIV  and  XV  contain  the  number  of  the  spring  used,  the 
extension  of  the  spring  as  measured  on  the  trace  in  inches,  the  corresponding 
pull  of  the  spring,  measured  in  grammes,  as  taken  from  the  calibration  curves, 
and,  lastly,  the  computed  pressure  on  the  plane,  obtained  by  multiplying  the  pull 
of  the  spring  by  the  factor  0.524,  which  reduces  the  effect  of  the  actually  unequal 
arms  of  the  instrument  to  what  it  would  have  been  were  the  arms  equal.  For 
angles  of  90°  the  instrument  affords  an  additional  method  of  determining  the 
constant  of  normal  pressure,  and  for  all  these  observations  the  resulting  values 
of  km  and  k  have  been  computed.  As  previously  used,  the  numerical  value  of  k 
relates  to  velocities  expressed  in  feet  per  second  and  pressure  in  pounds  per 
square  foot,  and  km  relates  to  velocities  -expressed  in  meters  per  second  and 
pressures  expressed  in  grammes  per  square  centimeter. 

The  horizontal  pressures  on  the  inclined  planes  diminish  with  decreasing 
angles  of  elevation,  and  for  angles  of  5°  and  under  are  less  than  100  grammes. 
.  Now,  for  a  pressure  less  than  100  grammes,  or  even  (except  in  very  favorable 
circumstances)  under  200  grammes,  the  various  errors  to  which  the  observations 
are  subject  become  large  in  comparison  with  the  pressure  that  is  being  measured, 
and  the  resulting  values  exhibit  wide  ranges.  In  such  cases,  therefore,  the 
measured  pressures  are  regarded  as  trustworthy  only  when  many  times  repeated. 
On  the  30  x  4.8  inch  plane,  weight  500  grammes,  fifteen  observations  of  horizontal 
pressure  have  been  obtained  at  soaring  speeds.  These  values  have  been  plotted 
in  Fig.  11,  and  a  smooth  curve  has  been  drawn  to  represent  them  as  a  whole. 
For  angles  below  10°  the  curve,  however,  instead  of  following  the  measured 
pressure,  is  directed  to  the  origin,  so  that  the  results  will  show  a  zero  horizontal 

*  For  a  further  analogy  with  a  corresponding  reversal  in  the  position  of  the  center  pressure,  see  Appendix  C. 

t  Only  after  completing  these  experiments  has  my  attention  been  called  to  those  of  Hutton,  who  appears  to 
have  been  the  first  to  make  experiments  in  this  field,  in  1787,  and  who,  it  is  interesting  to  see,  appreciated  the 
necessity  of  examining  this  question  of  aspect.  He  tried  a  plane  8x4  inches  with  both  the  long  edge  and  the 
short  edge  in  the  direction  of  the  arms  of  his  whirling  machine,  but  failed  to  obtain  any  sensible  difference  in 
his  resulting  horizontal  pressure,  probably  because  the  friction  of  his  apparatus  swallowed  up  the  small  differ- 
ences that  exist  in  the  horizontal  component  of  the  pressure  at  small  angles.  If  he  had  measured  the  total 
pressure  or  the  vertical  component,  he  would  probably  have  discovered  a  difference  in  the  two  cases.  I  also 
flnd  that  while  my  experiments  have  been  in  progress,  Mr.  W.  H.  Dines  has  likewise  been  investigating  the 
effect  of  aspect,  at  Hersham,  England,  with  results  similar  to  my  own. 


64 


EXPERIMENTS    IN    AERODYNAMICS. 
FIG.   11. 


500 

inn 

—  i 

/< 

• 

/ 

W\i 

300 
200 
100 
0 

/ 

/ 

i 

/ 

/ 

/ 

- 

*< 

4 

LV\ 

i 

i         jf 

/ 

o0 

)             ^r 

>       ^r 

/ 

/ 

r 

S                 10 

5                  20                 as                  30                  38                  40                  4 

Horizontal  pressure  (or  resistance  to  advance)  on  30  x  4.8  inch  plane  at  soaring  speeds 

obtained  with  the  Component  Pressure  Recorder. 
Abscidsae :  =  Angles  of  inclination  («)  of  plane  to  horizon. 
Ordinates :  =  Horizontal  pressure  (R)  in  grammes. 
Q  Represents  points  observed. 
X  Represents  pointe  given  by  equation,  R  =  weight  X  tangent  a. 


THE   COMPONENT    PRESSURE    RECORDER  65 

pressure  for  a  zero  angle  of  inclination.  This,  of  course,  must  be  the  case  for  a 
plane  of  no  thickness,  and  cannot  be  true  for  any  planes  of  finite  thickness  with 
square  edges,  though  it  may  be  and  is  sensibly  so  with  those  whose  edges  are 
rounded  to  a  so-called  "fair"  form.  Now,  the  actual  planes  of  the  experiments 
presented  a  squarely-cut  end-surface  one-eighth  of  an  inch  (3mm.2)  thick,  and 
for  low  angles  of  inclination  this  end-surface  is  practically  normal  to  the  wind. 
Both  the  computed  pressures  for  such  an  area  and  the  actually  measured 
pressures,  when  the  plane  is  set  at  0,  indicate  conclusively  that  a  large  por- 
tion of  the  pressures  measured  at  the  soaring  speeds  of  2°,  3°,  and  5°  is  end 
pressure,  and  if  this  be  deducted,  the  remaining  pressure  agrees  well  with  the 
position  of  the  curve.  The  observed  pressures,  therefore,  when  these  features 
are  understood,  become  quite  consistent.  The  curve  represents  the  result  obtained 
from  these  observations  for  the  horizontal  pressure  on  a  plane  with  "fair "-shaped 
edges  at  soaring  speeds. 

A  comparison  of  this  experimental  result  can  now  be  made  with  the  formula, 
which  appears  to  be  nothing  else  than  an  expression  for  a  simple  resolution  of 
forces.  I  say  "  appears,"  since  error  is  so  subtle  in  its  intrusion  in  these  cases 
that  I  have  preferred  to  give  the  matter,  even  here,  experimental  confirmation. 

From  the  analysis  above  given  we  have  the  equation  R  =  W  tan  a*W  being 
the  vertical  component  of  pressure  which,  at  the  instant  of  soaring,  is  the  weight 
of  the  plane.  For  the  purpose  of  comparing  the  points  given  by  this  equation 
with  the  curve  deduced  from  the  observed  pressures,  the  former  are  shown  by 
crosses  on  the  diagram  with  the  curve.  The  agreement  between  the  two  is 
remarkably  close,  and,  according  to  the  standpoint  from  which  the  subject  is 
viewed,  we  may  say  that  the  formula  is  actually  identifiable,  as  it  appears  to  be, 
with  a  simple  case  of  the  resolution  of  forces,  or  that  the  accuracy  of  the  har- 
monized experiments  is  established  by  their  accordance  with  an  unquestioned 
law  of  mechanics. 

WORK  NECESSARY  TO  BE  EXPENDED  IN  FLIGHT. 

Having  now  obtained  final  values  for  the  horizontal  pressure,  or  the  resist- 
ance to  the  horizontal  advance  of  inclined  planes,  and  having  determined  their 
soaring  speeds  at  different  angles  of  inclination,  the  work  necessary  to  be  expended 
per  minute  in  propelling  such  planes  through  the  air  is  given  in  kilogrammeters 
.by  the  expression  605  F,  R  being  the  horizontal  pressure  in  grammes,  and  V 
the  soaring  speed  expressed  in  meters  per  second. 

The  following  table,  XIII,  contains  a  computation,  for  the  case  of  the  30"  x  4.8 
inch  plane  weighing  500  grammes,  of  the  work  necessary  to  be  expended  per 
minute,  the  values  of  R  being  taken  from  the  curve  of  figure  11 : 

*Note  to  Second  Edition.     According   to  what  has  been    said,  this  is  only  true  for  different  angles  of 
the  same  plane  under  the  same  aspect.     (See  p.  60.) 


66 


EXPERIMENTS    IN    AERODYNAMICS 
TABLE  XIII. 


Angle  with 

Soaring  speed 
V. 

Horizontal 
pressure 
B. 

Work  expended  per 
minute 
60RV. 

Weight  with  planes  of  like 
form  that  1  horse-power 
will    drive  through  the 
air  at  velocity  V. 

[Note    to    sec- 
ond edition.] 
R=Wtana 
R. 

a. 

(Observed.) 

(Calculated.) 

Meters 
per  second. 

Feet 
per  second. 

Grammes. 

Kilogram- 
meters. 

Foot- 
pounds. 

Kilo- 
grammes. 

Pounds. 

Grammes. 

45° 

11.2 

36.7 

500 

336 

2,434 

6.8 

15 

500. 

30 

10.6 

34.8 

275 

175 

1,268 

13.0 

29 

288. 

15 

11.2 

36.7 

128 

86 

623 

26.5 

58 

134. 

10 

12.4 

40.7 

88 

65 

474 

34.8 

77 

88.15 

5 

15.2 

49.8 

45 

41 

297 

55.5 

122 

43.75 

2 

20.0 

65.6 

20 

24 

174 

95.0 

209 

17.5 

This  table  shows  that  for  an  inclination  of  2°  the  velocity  of  flight  which 
suffices  for  soaring  is  20.0  meters  per  second,  and  that  the  work  expended  per 
minute  to  support  the  plane  (weighing  500  grammes)  is  24  kilogrammeters,  or  174 
foot-pounds.  The  7th  and  8th  columns  contain  the  weight  with  planes  of  like  form 
that  one  horse-power  will  drive  through  the  air  at  velocity  V.  At  2°  this  is  95 
kilogrammes,  or  209  pounds.  This,  strictly  speaking,  holds  good  only  for  a  system 
of  planes  whose  weight,  inclusive  of  any  actual  motor  or  other  attached  weight,  is 
500  grammes  per  square  foot  of  inclined  plane  surface,  and  which  is  made. up  of 
30  x  4.8  inch  planes.  The  experiments  with  the  Plane-Dropper  show  that  in 
horizontal  flight  at  attainable  speeds,  a  system  of  such  planes  .can  be  made  by 
placing  one  above  the  other  at  a  distance  of  about  4  inches  without  any  sensible 
diminution  of  relative  efficiency.  Whether  these  relations  of  power,  area,  weight, 
and  speed,  experimentally  established  for  small  planes,  will  hold  good  in  the 
same  ratios  for  indefinitely  large  ones,  I  am  not  prepared  to  say ;  but  from  all 
the  circumstances  of  experiment,  I  can  entertain  no  doubt  that  they  do  so  hold, 
far  enough  to  afford  entire  assurance  that  we  can  thus  transport  (with  fuel  for  a 
considerable  journey)  weights  many  times  greater  than- that  of  a  man. 

The  preceding  investigation,  which  results  in  an  expression  for  the  varying 
amounts  of  work  done  by  an  elementary  aerodrome  driven  at  the  various  soaring 
speeds  corresponding  to  the  various  angles  given,  has  been  derived  for  the  case  in 
which  the  direction  of  propulsion  of  the  aerostat  is  horizontal  and  in  which  its 
plane  makes  an  angle  a  with  the  horizon.  In  the  case  of  an  actual  aerodrome, 
however,  it  will  very  probably  be  found  advantageous  to  propel  it  in  the  line  of 
its  plane  at  such  an  angle  (in  practice  a  very  small  angle)  that  the  resultant 
forward  motion  due  to  this  elevation  and  to  the  simultaneous  action  of  gravity 
will  be  exactly  horizontal.  If  in  this  case  its  horizontal  velocity  be  represented 
by  V,  the  work  done  per  unit  of  time  will  be  expressed  by  the  product  of  the 


THE   COMPONENT   PRESSURE    RECORDER.  67 

weight  multiplied  by  V  tan  a,  the  latter  factor  being  the  height  H  to  which  the 
plane  is  virtually  lifted  against  gravity. 

It  will  be  seen,  now,  that  this  expression  is  the  same  as  that  derived  for  the 
former  case,  V  being  the  horizontal  forward  velocity,  and  a  the  inclination  of  the 
plane  to  the  horizon.  In  order  to  prove  the  perfect  identity  of  significance  of 
the  two  expressions  it,  would,  however,  remain  to  show  experimentally  that  the 
relation  of  V  to  a  in  this  new  case  is  the  same  as  that  experimentally  derived  for 
the  first  case.  I  have  made  no  experiments  with  which  to  determine  this  relation, 
but  I  may  say  that,  since  all  the  circumstances  of  the  resulting  motion  seem  the 
same  in  the  one  case,  as  in  the  other,  the  relation  between  F  and  a  is  presumably 
the  same,  and  consequently  the  amount  of  work  done  in  the  second  case  is 
presumably  the  same  as  that  done  in  the  first  case ;  it  is  certainly  so  nearly  so 
that  whenever  a  is  small  (and  it  always  is  so  in  such  economic  or  horizontal  flight), 
we  may,  for  all  practical  purposes,  assume  an  identity  of  the  two  cases.  It  fol- 
lows that,  in  soaring  with  (horizontal)  velocity  F,  the  direction  of  propulsion  can 
vary  between  0°  and  a°  at  will,  without  sensibly  changing  the  amount  of  work 
that  is  expended,  so  long  as  the  plane  remains  at  the  angle  a  with  the  horizon. 

The  reader  who  has  followed  the  description  of  this  instrument  will  see  that 
the  experiments  have  consisted  in  measuring  with  a  dynamometer  the  actual 
resistance  to  motion  experienced  by  planes  when  just  "soaring"  or  supporting 
themselves  under  all  the  circumstances  of  flight  in  free  air,  except  that  the  plane 
is  restricted  from  the  "  flouncing  "  caused  by  irregular  currents,  etc.,  and  made 
to  hold  a  steady  flight. 

The  most  important  conclusion  may  be  said  to  be  the  confirmation  of  the 
statement  that  to  maintain  such  planes  in  horizontal  flight  at  high  speeds,  less  power 
is  needed  than  for  low  ones. 

In  this  connection  I  may  state  the  fact,  surely  of  extreme  interest  in  its 
bearing  on  the  possibility  of  mechanical  flight,  that  while  an  engine  developing 
one  horse-power  can,  as  has  been  shown,  transport  over  200  pounds  at  the  rate 
of  20  meters  per  second  (45  miles  an  hour),  such  an  engine  (i.  e.,  engine  and 
boiler)  can  be  actually  built  to  weigh  less  than  one-tenth  of  this  amount. 


68 


EXPERIMENTS    IN    AERODYNAMICS. 


Experiments  with  the  Component  Pressure  Recorder  to  measure  the  horizontal  pressure  on  normal  and  inclined  planes 

and  to  determine  their  soaring  speeds. 

TABLE  XIV— FIRST  SERIES. 
F.  W.  VERY,  Conducting  experiments ;  JOSEPH  LUDEWIG,  Regulating  engine. 


Date. 

Mean  barometer 
(millimeters). 

Mean   temperature 
(centigrade). 

Mean  wind  velocity 
(meters  per  second). 

1890. 

7410 

14° 

030 

7386 

17 

1  20 

"             2      

7366 

18 

050 

"            3  

7358 

15 

055 

"             4                 

7345 

19 

060 

«             7                

7277 

15 

060 

"            8  

736.6 

15 

0.30 

"            9  

740.1 

17 

0.50 

Date. 

Description  of  planes. 

Angle  of  elevation  o. 

Attitude  of  plane. 

P* 

<3^§ 

£§» 

§-*£ 

|"ft 

Number  of  spring. 

Extension  of  spring 
(inches). 

Pull  of  spring 
(grammes). 

Horizontal  pressure 
on  plane  R  (gram's). 

Km. 

k, 

1890. 
Sept  29 

cm.        cm. 
24  x  6  inches  (61  0  x  15  2) 

30° 

120 

4 

1.20 

708 

371 

(i 

Weight  500  grammes 

15 

Soaring  

122 

4 

0.30 

294 

154 

« 

10 

ii 

136 

4 

0.20 

229 

120 

Oct.     1 

cm.        cm. 
24  x  6  inches  (61.0  x  15.2) 

90 

9.6 

4 

2.80 

1,358 

712 

.0083 

.0015S 

a 

Weight  250  grammes 

30 

Soaring 

78 

4 

<( 

30 

78 

9 

131 

294 

154 

M 

15 

i 

83 

a 

064 

164 

86 

Get      2 

30 

i 

79 

U 

125 

284 

149 

it 

15 

i 

80 

ll 

it 

10 

i 

86 

u 

050 

134 

70 

ii 

5 

« 

118 

ll 

045 

121 

63 

ii 
it 

3 
8 

Not  quite  soaring 
Soarin^  

13.3 
15.4 

ll 

ll 

0.35 
0.39 

101 

107 

53 
56 

tt 

fl 

(i 

17.6 

ll 

0.41 

113 

59 

ii 

0 

Not  soaring  

25.0 

ll 

0.50 

134 

70 

Oct.     3 

cm.        cm. 
24  x  6  inches  (61.0  x  15.2) 

90 

6.7 

4 

0.88 

567 

297 

.0071 

.00135 

n 

Weight,  1,000  grammes. 

90 

7.2 

i 

1.21 

708 

371 

.0077 

.0014G 

it 

90 

9.8 

i 

2.80 

1.358 

712 

.0079 

.00151 

d 

30 

Soaring  . 

152 

i 

160 

867 

454 

n 

15 

n 

162 

i 

095 

594 

311 

n 

10 

ii 

19.4 

i 

0.68 

480 

252 

H 

fi 

Not  soaring  .  .  . 

25.0 

n 

0.50 

397 

208 

THE   COMPONENT    PRESSURE    RECORDER. 


69 


TABLE  XIV— Continued. 


Date. 

Description  of  planes. 

Angle  of  elevation  a. 

Attitude  of  plane. 

JB 
<5  "o> 
gJ3,^ 

o      ""C 

ll| 
2 

Number  of  spring 

Extension  of  spring 
(inches). 

Pull  of  spring 
(grammes). 

Horisontal  pressure 
on  plane  R  (gram's). 

km. 

k. 

1890. 
Oct      3 

cm.        cm. 
12  x  12  inches  (30  5  x  30.5) 

10 

95 

4 

2.70 

1325 

694 

0083 

00157 

it 

Weight  500  grammes. 

90 

8.3 

u 

1.84 

970 

508 

0079 

00150 

ti 

30 

Soaring  

9.5 

It 

0.75 

510 

267 

it 

15 

u 

12.0 

It 

0.27 

271 

142 

it 

10 

;C 

150 

tl 

0.12 

159 

83 

U 

10 

(1 

146 

9 

0.80 

197 

103 

u 

5 

II 

200 

n 

0.70 

176 

92 

u 

cm.        cm. 
12  x  12  inches  (30  5  x  30  5) 

90 

62 

ti 

2.20 

471 

247 

0069 

00132 

u 

Weight,  250  grammes. 

30 

Soarin°f.  .  . 

66 

It 

1.02 

242 

127 

a 

15 

91 

tl 

0.49 

130 

68 

a 

10 

t 

106 

11 

0.45 

120 

63 

a 

5 

! 

146 

U 

0.35 

100 

52 

it 

3 

t 

167 

tl 

0.40 

113 

59 

» 

t 

188 

It 

0.55 

145 

76 

a 

Oct.     4 

cm.        cm. 
12  x  12  inches  (30.5  x  30.5) 

0 
90 

Not  soaring  .... 

23.1 
70 

It 

4 

0.80 
1.25 

199 

726 

104 
380 

0084 

00160 

u 

Weight,  1,000  grammes. 

90 

94 

u 

2.48 

1  235 

647 

0079 

00150 

u 

30 

Soaring.  . 

12.8 

n 

1.85 

970 

508 

u 

30 

12.8 

it 

1.80 

953 

499 

I! 

15 

u 

174 

u 

0.57 

435 

228 

Oct.     3 

15 

it 

167 

9 

1.75 

388 

203 

U 

10 

it 

200 

II 

1.25 

285 

149 

tt 

5 

it 

255 

u 

0.80 

199 

104 

Oct.     7 

cm.        cm. 
6  x  24  inches  (15.2  x  61.0) 

90 

62 

u 

2.65 

563 

295 

0081 

.00155 

if 

Weight,  250  grammes. 

30 

Soaring  

76 

i 

1.35 

308 

161 

It 

15 

118 

t 

0.90 

216 

113 

« 

10 

u 

141 

i 

0.60 

155 

81 

(1 

5 

tt 

21  1 

i 

0.90 

216 

113 

U 
if 

cm.        cm. 
6  x  24  inches  (15.2  x  61.0) 

3 

90 

Nearly  soaring  .  . 

25.0 
63 

i 

u 

1.00 
2.70* 

235 

571* 

123 

299*| 

0081* 

00154* 

« 

Weight,  500  grammes. 

90 

54 

It 

2.08 

453 

237 

0089 

00169 

(1 

90 

41 

u 

110 

256 

134 

0085 

00161 

it 

30 

Soaring  

105 

It 

230 

492 

258 

« 

15 

152 

11 

100 

235 

123 

(t 

10 

u 

207 

u 

085 

206 

108 

U 

5 

u 

273 

It 

065 

166 

87 

u 

cm.        cm. 
6  x  24  inches  (15.2  x  61.0) 

90 

73 

4 

170 

909 

476 

0096 

00189 

* 

Weight,  1,000  grammes. 

90 

57 

11 

095 

597 

313 

0103 

00197 

.1 

30 

Soaring.  . 

146 

11 

180 

953 

499 

•' 

15 

uaiiiig 

214 

It 

060 

450 

236 

it 

10 

u 

27.3 

It 

0.30 

294 

154 

*  Trace  was  at  limit  of  admissible  extension,  and  hence  the  correct  results  are  greater  than  these  values. 


70 


EXPERIMENTS    IN    AERODYNAMICS. 
TABLE  XIV— Continued. 


Date. 

Description  of  planes. 

Angle  of  elevation  «. 

Attitude  of  plane. 

•SB 

M.3 
11 

|£f 
<3^§ 

*8§ 
111 

|- 

Number  of  spring. 

Extension  of  spring 
(inches). 

Pull  of  spri  ng 
(grammes). 

Horizontal  pressure 
on  plane  R  (gram's). 

km- 

k. 

1890. 
Oct.     8 

cm.       cm. 
6  x  24  inches  (15.2  x  61.0) 

15 

Soaring  

21.8 

i 

tt 

Weight,  1,000  grammes. 

10 

a 

28.6 

u 

6 

Not  soaring  

30.0 

0.40 

113 

59 

u 

cm.       cm. 
30x4.8  inches  (76.2  x  12.2) 

90 

5.0 

1.40 

317 

166 

.0073 

.00138 

(i 

Weight,  500  grammes. 

90 

6.0 

2.20 

471 

247 

.0075 

.00142 

u 

90 

6.2 

2.45 

527 

276 

.0076 

.00145 

u 

30 

Soaring  

10.6 

2.30 

492 

258 

u 

10 

u 

17.9 

0.75 

183 

96 

u 

10 

u 

12.1 

0.90 

216 

113 

u 

ft 

15.2 

0.45 

122 

64 

it 

8 

Not  soaring  

21.1 

0.50 

134 

70 

it 

0 

25.0 

0.90 

216 

113 

u 

cm.       cm. 
30  x  4  8  inches  (76.2  x  12.2) 

90 

58 

u 

2.60 

554 

290 

.0091 

.00173 

ii 

Weight,  250  grammes. 

90 

43 

II 

1.20 

277 

145 

.0086 

.00163 

u 

RO 

Soaring  

81 

II 

1.30 

294 

154 

u 

15 

i» 

83 

u 

0.50 

134 

70 

u 

10 

u 

93 

11 

0.35 

100 

52 

u 

5 

u 

133 

(I 

0.40 

113 

59 

ii 

3 

u 

17  1 

(I 

0.55 

145 

76 

ii 

9 

261 

II 

0.50 

134 

70 

ii 

0 

222 

II 

1.20 

277 

145 

u 

0 

279 

II 

150 

336 

176 

Oct      9 

cm.        cm. 
30  x  4  8  inches  (76  2x122) 

90 

58 

4 

0.7 

490 

257 

.0082 

.00157 

u 

Weight  1  000  grammes. 

90 

83 

u 

1.7 

909 

476 

.0074 

.00141 

u 

;i 

30 
15 

Soaring  

u  ' 

15.2 
17.1 

u 

ii 

2.2 
1.1 

1110 
659 

581 
345 

u 

15 

u 

17.4 

?, 

2.3 

492 

258 

ii 

10 

u 

17.9 

4 

u 

10 

ii 

18.2 

9, 

1.9 

416 

218 

u 

ft 

II 

22.6 

u 

1.6 

355 

186 

Average  of  22  determinations  of  km  (at  mean  temperature,  16°  C.)  =  .00816. 


THE   COMPONENT    PRESSURE    RECORDER. 


71 


TABLE    XV— SECOND    SERIES. 

NOVEMBER  25, 1890. — F.  W.  VERY,  Conductor  of  experiments. 
Barometer,  730  mm. ;  temperature,  10°.0  C. ;  wind  velocity,  2.4  meters  per  second. 


a' 

•S.E 

W 

bo 

f-l     CO 

g 

£^ 

bb 

•§ 

a 

a  «2 

o 

Q}    CJ 

C 

"*** 

ffi 

••& 

£3  S 

OQ 

/^~^ 

O    g 

$ 

S*""'^ 

GO 

t*-(  tn 

!D    £ 

Onx59 

Description  of  planes. 

r2 

Attitude  of  plane. 

*S^    0 

^0 

flU 

a 
*«  a 

^(^ 
^    (p 

Remarks. 

(M 

fc*i  0}    f 

b 

o  .c 

O   03 

O 

'o    03   ?n 

,0 

s^ 

M 

|J 

f 

O  ^   ® 

r^J     &,  &, 

a 

£ 

H 

^ 

o  g 

>• 

^ 

d< 

24  x  6  in.  (24  in.  side 

45° 

Soaring  

10.9 

4 

2.10 

907 

476 

horizontal). 

50 

tt 

11.2 

4 

2.50 

1,070 

560 

Weight,  500  grammes. 

5 

tt 

16.9 

4 

5 

tt 

17.2 

3 

0.38 

82 

43 

3 

Not  Quite  soaring 

19.4 

Adopt  19.6  for  soaring  speed. 

30 

Soaring  

10.6 

4 

1.10 

499 

261 

10 

(i 

13.3 

4 

0.21 

91 

48 

Too  small  extension  of  spring 

to  give  reliable  pressure. 

NOVEMBER  26, 1890. — F.  W.  VERY,  Conductor  of  experiments. 
Barometer,  736  mm. ;  temperature,  0°.0  C. ;  wind  velocity,  0.3  meters  per  second. 


a 

'o  S 

bo 

SH  /QQV 

o 

-2~§ 

g3 

S 

"C 

PH 

C 

1| 

'•§ 

fl  a  ^ 

•c 

CD 

—  /OQV 

Description  of  planes. 

03 

! 

'o 

Attitude  of 
plane. 

&a  ™ 

OH 
O 

<+-<  ^ 
O    <13 

a-S 

o  a 

"-<  «rH 
O3  V  • 

00  S 

fA 

0    g 

o  bB 

f^-^s 

•S  2 

G  ^ 

... 

k. 

Remarks. 

QJ 

"o   c3    ^ 

^O 

a 

(  v^5* 

N  ^^ 

"bb 

O  -^  % 

a 

-S 

•—  t 

•  rH      A 

a 

> 

1 

g 

(S 

w§ 

24  x  6  in.  (24  in.  side 

0° 

16.6 

3 

0.10 

27 

14 

horizontal). 

2 

183 

3 

0.40 

82 

43 

Weight,  500  grammes. 

3 

Soaring  .  .  . 

16.2 

3 

0.45 

86 

45 

5 

"       ... 

14.4 

3 

0.57 

100 

52 

90 

9.03 

4 

2.50 

1,068 

558 

.0074 

.00141 

90 

7.41 

4 

1.70 

749 

392 

.0077 

.00146 

Same  plane  (6  in.  side 

90 

7.99 

4 

1.85 

803 

421 

.0071 

.00136 

horizontal). 

90 

5.86 

4 

0.97 

454 

238 

.0075 

.00142 

6x6  inches. 

90 

17.96 

4 

2.40 

1,021 

534 

.0071 

.00136 

Weight,  125  grammes. 

90 

16.74 

4 

2.05 

'885 

464 

.0071 

!00136 

3 

Soaring  .  .  . 

20.1 

3 

0.50 

91 

48 

5 

it 

18.7 

3 

0.60 

100 

52 

10 

tt 

15.0 

3 

0.73 

113 

59 

72 


EXPERIMENTS    IN    AERODYNAMICS. 


TABLE  XV — Continued. 


Description  of  planes. 

Angle  of  elevation  a. 

Attitude  of 
plane. 

•SB 

It 

o      'O 
o^I 

*88 

'3  &  £ 

•ras. 

> 

Number  of  spring. 

Extension  of  spring 
(inches). 

Pull  of  spring 
(grammes). 

Horizontol  pressure 
on  plane  R  (gram's). 

/Ljn* 

k. 

Remarks. 

12  x  12  inches. 

0 

16.7 

3 

0.35 

77 

40 

Weight,  500  grammes. 

0 

17.8 

8 

0.40 

84 

44 

2 
2 
3 

)  Not  soar- 
j      ing. 
Nearly 

20.7 
16.7 
209 

3 
3 

3 

0.70 
0.55 
1  00 

109 
95 
131 

57 
50 
69 

Adopt  21.4  m.  per  sec. 

5 
10 

20 

soaring. 

Soaring.  .  . 
a 

« 

20.1 
15.8 
11  1 

3 
3 
3 

1.30 
1.70 

152 
180 

80 
94 

as  probable  soaring 
speed. 

Spring     extended     to 

20 
30 
45 
90 

a 
u 

it 

11.1 
8.9 
10.2 
823 

4 
4 
4 
4 

0.75 
1.20 
2.31 
2.20 

340 
345 
985 
939 

178 
285 
516 
4991 

.0078 

.00148 

limit. 

90 

845 

4 

2.28 

976 

511 

.0077 

.00146 

90 

915 

4 

270 

1,135 

595 

.0077 

.00146 

90 

811 

4 

2.00 

863 

45?, 

.0074 

.00141 

12  x  6  in  (12  in  side 

0 

186 

8 

0.55 

95 

50 

h  orizontal) 

3 

S  carcel  y 

188 

3 

067 

107 

56 

Probable  soaring  speed, 

Weight,  250  grammes. 

5 
10 
20 
20 
30 
45 
90 

soaring. 

Soaring.  .  . 

t 

i 

i 

< 
< 

17.5 
13.3 
10.8 
11.0 
10.5 
10.9 
7.78 

3 
3 
3 
4 
4 
4 
4 

0.78 
1.00 
1.75 
0.33 
0.77 
1.14 
0.83 

115 
131 
182 
159 
347 
522 
399 

60 
69 
95 
83 
182 
273 
909 

.0074 

.00141 

19.2  m.  per  sec. 

90 

909 

4 

1.21 

549 

9,88 

.0075 

.00142 

90 

10.89 

4 

1.98 

862 

459, 

.0082 

.00156 

90 

12.50 

4 

2.55 

1,089 

571 

.0079 

.00150 

90 

11.19 

4 

2.02 

871 

456 

.0079 

.00149 

90 

10.00 

4 

1.60 

704 

369 

.0079 

.00151 

90 

8.14 

4 

1.00 

463 

943 

.0079 

.00150 

30x4.8  in.  (30  in.  side 

0 

17.9 

8 

0.30 

72 

38 

horizontal). 
Weight,  500  grammes. 

2 
3 
5 
10 
20 

Soaring.  .  . 
« 

<t 
a 

20.1 
17.8 
15.2 
12.6 
11.7 

3 
3 
3 
3 
8 

0.90 
1.04 
1.12 
1.92 
3.34 

125 
134 
138 
197 
300 

65 
70 
72 
103 
157 

20 

116 

4 

0.70 

295 

155 

30 
45 
90 

Soaring  .  .  . 
« 

10.8 
11.2 
839 

4 
4 
4 

1.21 
2.12 
2.20 

550 
912 
935 

288 
478 
490 

.0075 

.00143 

90 

1026 

4 

330 

1,380 

723 

.0074 

.00141 

90 

800 

4 

205 

885 

464 

.0078 

.00148 

THE   COMPONENT   PRESSURE    RECORDER. 

TABLE  XV — Continued. 

DECEMBER  5,  1890. — F.  W.  VERY,  Conductor  of  experiments. 
Barometer,  732  mm. ;  temperature,  + 1°.0  C. ;  wind  velocity,  light. 


i 

i 

*£  S 
t-t  ,4^ 

la 

t 

to 

•c 

Bi 

00       . 

t>0 

a 

>ressure 
gram's). 

ascription  of  plane. 

> 

o 

Attitude  of  plane. 

•s^l 

00 

O 

O    Q> 

"1 

HKv_, 

Remarks. 

'o 

£>§  ™ 

°   §3 

£  £3 

u 

'o'&o, 

'g 

1 

|Z!^ 

•3  T^i 

a 

O 

> 

J5 

I 

Pi 

°  o 

2  x  12  inches. 

10° 

More  than  soaring. 

15.8 

r  eight  500  grammes 

10 

Soarin"  

150 

3 

180 

191 

100 

Flange  of  cone-pulley  broke  and  stopped  observations  for  the  day. 

DECEMBER  6,  1890. 
Barometer,  730  mm. ;  temperature,  +  2°.5  C. ;  wind  velocity,  calm. 


o 

a 
o 
IB 

•SB 

l! 

•r* 

Jf 

1^ 

c 

11 

1 

O        *"CJ 

a 

00 

O    O 

"*! 

0,v2S 

Description  of  planes. 

•3 

Attitude  of  plane. 

"o^  o 

•8 

pi's 

««  a 

•3°^ 

Remarks. 

<*H 

O  (3 

o 

B 

'CD  ^O 

tlD 

•3, 

'o    &   t! 

X  r-H     O 

^o  p,  p, 

a 

1 

•gU 

1 

> 

0 

PH 

°   O 

12  x  12  inches. 

20° 

Soaring  

12.8 

3 

2.60 

245 

128 

Velocity  of  soaring  not  so  well 

\V  eight,  500  grammes. 

determined    as    on    Novem- 

ber 26. 

20 

(C 

12.6 

4 

Velocity  of  soaring  not  so  weD 

determined    as    on    Novem- 

30 

(1 

10.3 

4 

1.10 

500 

262 

ber  26. 

45 

u 

11.4 

4 

2.20 

939 

492 

Velocity  of  soarin°"  not  so  ac- 

45 

Not  soaring  

10.0 

4 

L82 

794 

416 

curately    determined    as    on 

30 

a             (. 

10.0 

4 

0.85 

408 

214 

November  26. 

30 

(C                Ck 

10.0 

4 

0.75 

340 

178 

20 

(I           11 

10.0 

3 

i!oo 

131 

69 

30  x  4.8  inches. 

5 

Not  quite  soaring  . 

14.3 

14.9  meters  per  second  assumed 

Weight,  500  grammes. 

as  soaring  speed. 

Fine  mist  throughout  the  observations. 


10 


74 


EXPERIMENTS    IN   AERODYNAMICS. 


TABLE  XV — Continued. 

DECEMBER  11,  1890. — F.  W.  VERY,  Conductor  of  experiments.   . 
Barometer,  724  mm. ;  temperature,  +  5°  C. ;  wind  velocity,  0.8  meters  per  second. 


B 

•SB 

| 

bo 

g 

§5°* 

g 

t-t    4-3 

bo 

m  s 

a 

CH 

£ 

°^   o3 

Description  of  planes. 

of  elevat 

Attitude  of 
plane. 

g££ 

-U     £>     *° 

a 

00 

'S 

h 

a> 

00      . 
O    O 

o  c 
•fie/ 

of  sp 
grammes; 

^^ 

"^  § 

kin- 

i. 

Remarks. 

o> 

% 

•§^1 

^ 

s 

C 

^^  ^-^ 

N  ""TV 

Jftft 

3 

| 

s 

PH 

M° 

30  x  4  8  in  (30  in  side 

qo° 

830 

1 

180 

930 

487 

.0076 

0.00144 

horizontal) 

90 

915 

1 

220 

1098 

576 

.0074 

0.00140 

Weight,  500  grammes. 

45 

Soaring.  .  .  . 

11.3 

1 

2.10 

1,057 

553 

KO 

1 

091 

557 

292 

20 

tt 

10.9 

1 

0.47 

350 

183 

15 

"         .... 

11.1 

3 

0 

207 

g 

020 

59 

31 

24  x  6  in  (24  in  side 

0 

207 

R 

020 

59 

31 

horizontal). 

10 

Soaring  .... 

13.0 

Weight,  500  grammes. 

Mean  of  22  determinations  of  km  (at  temperature  0°  C.)  =  0.0076. 


CHAPTER   VII. 

THE   DYNAMOMETER-CHRONOGRAPH. 

Having  determined  by  means  of  the  Component- Recorder  the  resistance  that 
must  be  overcome  in  moving  a  material  plane  horizontally  through  the  air  at 
different  speeds,  the  next  step  of  my  investigation  has  consisted  in  devising  means 
for  measuring  the  power  that  must  be  put  out  by  a  motor  in  doing  this  useful 
work ;  for,  by  any  form  of  aerial  propulsion,  the  useful  work  that  can  be  derived 
from  the  motor  is  only  a  percentage,  either  large  or  small,  of  that  which  is 
expended.  It  becomes  important,  therefore,  to  determine  the  ratio  between  the 
propelling  force  obtained,  and  the  amount  of  power  that  must  be  expended  in  any 
given  case. 

In  devising  the  following  apparatus  I  have  confined  my  attention  to  aerial 
propellers  for  reasons  of  present  convenience,  and  not  because  I  think  them  the 
only  practicable  method  of  propulsion,  although  they  are  undoubtedly  a  most 
important  one. 

If  we  consider  the  actual  circumstances  of  such  experiments,  where  the  motor 
under  investigation  is  mounted  at  the  extremity  of  the  large  turn-table  arm  and 
is  in  motion,  frequently  at  a  rate  of  over  a  mile  a  minute,  and  that  the  end  of 
this  slender  arm  is  30  feet  from  any  solid  support  where  an  observer  might  be 
stationed,  it  will  be  seen  that  the  need  of  noting  at  every  moment  the  action  of 
apparatus,  which  under  such  circumstances  is  inaccessible,  imposes  a  difficult 
mechanical  problem.  After  trying  and  dismissing  other  plans,  it  became  evident 
that  a  purely  automatic  registry  must  be  devised  which  would  do  nearly  all  that 
could  be  supposed  to  be  done  in  the  actually  impracticable  case  of  an  observer 
who  should  be  stationed  at  the  outer  end  of  the  whirling  arm  beside  the  apparatus, 
which  we  may  suppose  for  illustration  to  be  an  aerodrome  moved  by  a  propeller. 
The  registering  instrument  for  the  purposes  desired  must  indicate  at  every 
moment  both  the  power  expended  on  the  supposed  aerodrome  to  make  it  sustain 
itself  in  flight,  and  also  the  portion  of  that  power  which  is  utilized  in  end-thrust 
on  the  propeller  shaft,  driving  the  model  forward  at  such  a  rate  as  to  maintain 
soaring  flight,  under  the  same  circumstances  as  if  it  were  relieved  from  all 
constraint  and  actually  flying  free  in  a  horizontal  course  in  the  air.  For  this 
purpose  a  peculiar  kind  of  dynamometer  had  to  be  devised,  which,  after  much 
labor  over  mechanical  difficulties,  finally  became  completely  efficient  in  the  form 

(76) 


76  EXPERIMENTS    IN    AERODYNAMICS. 

I  proceed  to  describe  and  which  I  have  called  the  Dynamo  meter -Chronograph. 
A  plan  of  the  instrument  is  given  in  plate  VIII.  Its  method  of  operation  in 
measuring  and  registering  (1)  the  power  expended  in  producing  rotation  and  (2) 
the  useful  result  obtained  in  end-thrust  is  here  separately  described. 

(1)  MEASUREMENT  OF  THE  POWER  EXPENDED. 

The  propeller  wheel  L,  which  is  to  be  investigated,  is  fastened  to  the  shaft 
SS',  which  becomes  its  axis,  and  is  driven  by  a  belt  running  from  the  pulley. 

When  the  pulley  is  driven  from  any  source  of  power,  the  1'esistance  offered 
by  the  air  to  the  rotation  of  the  propeller  develops  a  torsional  force  on  the  shaft 
SS'.  This  shaft  is  divided  into  two  portions  at  the  clock-spring  in  the  upper  end 
of  the  cylinder  D,  so  that  the  torsional  force  set  up  by  the  pulley  is  transmitted 
to  the  rest  of  the  axis  and  to  the  propeller  through  the  spring  in  question.  This 
torsional  force  can  and  does  cause  the  cylinder  E,  which  turns  with  the  propeller 
end  of  the  shaft,  to  be  twisted  with  respect  to  D,  which  rotates  with  the  pulley, 
until  the  force  is  balanced  by  the  winding  tension  of  the  clock-spring.  The  rela- 
tive angular  motion  between  the  pulley  and  the  shaft  S  causes  a  longitudinal 
motion  of  the  cylinder  E  into  the  cylinder  D,  by  means  of  a  spiral  groove  cut  in 
the  cylinder  D,  in  a  manner  which  is  sufficiently  shown  in  the  drawing,  so  that 
there  can  be  no  angular  movement  of  the  pulley  C  relative  to  the  shaft  and  to 
the  cylinder  E,  without  a  corresponding  longitudinal  motion  of  the  cylinder  E 
and  of  the  pencil  P",  which  registers  the  amount  of  this  longitudinal  motion 
on  the  recording  cylinder ;  and  it  will  be  observed  that  there  will  be  no  angular 
motion  and  no  linear  motion,  unless  work  is  being  done  by  the  pulley  ;  for,  if  the 
propeller  wheel  were  removed,  or  if  its  blades  were  set  with  their  planes  in  the 
planes  of  its  rotation,  however  fast  the  pulley  may  be  driven,  there  will  be  no 
record.  The  linear  motion  of  the  pen  P"  is,  then,  caused  by,  and  is  proportional 
to,  the  torsional  force  exerted  by  the  pulley,  and  to  this  only.  It  is  obvious  that 
if  the  recording  cylinder  revolve  at  a  known  rate,  the  pencil  trace  will  give  a 
complete  record  of  the  two  necessary  and  sufficient  factors  in  estimating  the  total 
power  put  out,  namely,  the  amount  of  this  power  from  instant  to  instant  (how- 
ever it  vary)  and  the  time  during  which  it  is  exerted  ;  the  former  being  given  by 
the  "  departure  "  of  the  pen  from  its  normal  position,  the  latter  by  the  length  of 
the  trace,  so  that  a  complete  indicator-diagram  showing  the  power  expended  is 
found  on  the  sheet  when  it  is  unrolled  from  the  cylinder.  The  abscissa  of  any 
point  in  the  developed  curve  is  proportional  to  the  time ;  its  ordinate,  which 
represents  the  departure  of  the  pencil  parallel  to  the  axis  of  the  cylinder,  is  pro- 
portional to  the  tension  of  the  clock-spring.  The  value  of  this  departure,  or  the 
actual  stress  it  represents,  after  allowing  for  all  circumstances  of  friction,  is 
obtained  by  calibrating  the  spring  by  hanging  weights  on  the  circumference  of 


THE   DYNAMOMETER-CHRONOGRAPH.  77 

the  pulley.  This  departure,  then,  corresponds  to  the  effect  of  a  definite  and 
constant  weight  so  applied,  so  long  as  we  use  the  same  spring  under  the  same 
adjustment.  When  widely  different  ranges  of  power  are  to  be  measured,  the 
additional  range  of  tension  required  is  obtained  with  the  same  spring  by  insert- 
ing a  set-screw  in  successive  holes,  numbered  0  to  15,  around  the  end  of  the 
cylinder  D,  so  as  virtually  to  shorten  or  lengthen  the  clock-spring.  A  separate 
calibration  is,  of  course,  required  for  each  setting. 

(2)   MEASUREMENT  OF  THE  END-THRUST. 

I  have  thus  far  spoken  of  the  shaft  or  axis  as  if  it  were  in  one  piece  between 
the  clock-spring  and  the  pulley,  but  for  the  purpose  of  measuring  the  end-thrust 
the  shaft  is  also  cut  in  two  within  the  cylinder  F.  The  two  pieces  are  maintained 
in  line  by  suitable  guides,  and  forced  to  rotate  together  by  a  fork  within  F,  but 
the  propeller  end  of  the  shaft  is  given  freedom  of  longitudinal  motion.  Any  end- 
thrust  on  the  axis,  whether  received  from  the  propeller  or  otherwise,  causes,  then, 
this  portion  carrying  the  pencil  P  to  slide  up  within  the  other  toward  the  pulley, 
telescoping  the  part  of  the  shaft  next  the  propeller  within  that  next  the  clock- 
spring,  and  causing  the  longitudinal  compression  of  the  spiral  spring  in  cylinder 
F,  as  shown  in  the  drawing.  All  the  parts  of  the  axis,  then,  between  the 
clock-spring  and  the  propeller  must  rotate  together  when  the  latter  is  revolved, 
but  the  end  of  the  axis  nearest  the  propeller,  and  this  end  only,  has  the 
capacity  not  only  of  rotatory  but  of  a  longitudinal  motion,  which  latter  is  per- 
mitted by  this  portion  of  the  axis  telescoping  into  the  other,  as  above  described. 
The  force  of  the  end-thrust  is  recorded  by  the  "departure"  of  the  pencil  P,  which 
bears  a  definite  relation  to  its  own  spring,  determined  by  independent  calibration. 
The  record  made  by  P  on  the  recording  cylinder  is  a  curve  whose  abscissae  are 
proportional  to  time  and  whose  ordinates  are  proportional  to  end-thrust.  This 
curve  cannot  by  itself  properly  be  called  an  indicator-diagram,  since,  taken 
alone,  it  records  a  static  pressure  only,  but  when  the  experiments  are  adjusted 
in  a  manner  later  described  in  this  chapter  the  record  of  the  speed  of  the  turn- 
table (on  which  it  will  be  remembered  this  apparatus  is  being  carried  forward) 
supplies  the  requisite  additional  data  that  an  indicator-diagram  demands.  Hence, 
while  the  pencil  P"  actually  traces  an  indicator-diagram  giving  the  expenditure 
of  power  at  every  moment,  the  pencil  P  traces  in  part  a  second  indicator-diagram 
giving  synchronously  the  useful  result  attained. 

A  third  pencil,  P',  records  the  seconds  of  a  mean  time-clock  through  the 
action  of  an  electro-magnet,  M,  and  obviously  gives  the  means  of  determining 
with  all  needful  precision  the  time  corresponding  to  each  element  of  angular 
rotation  of  the  cylinder,  even  should  this  vary.  This  time  record,  then,  serves 
two  purposes :  (1)  it  gives  the  speed  of  rotation  of  the  cylinder,  and  (2)  permits 


78  EXPERIMENTS    IN    AERODYNAMICS. 

the  traces  to  be  synchronized  with  the  speed  of  the  whirling  table  registered  on 
the  stationary  chronograph. 

The  cylinder  is  rotated  in  either  of  two  ways :  (first)  by  the  driving  pulley, 
through  a  system  of  gearing,  which  gives  the  cylinder  rates  of  rotation  equal  to 
TffW,  Wmr,  or  ToW  that  of  the  driving  pulley  according  as  desired,  so  that  the  speed 
of  the  pulley  is  thus  measured  by  the  rate  of  rotation  of  the  cylinder  ;  or  (second) 
the  cylinder  may  be  independently  rotated  by  an  attached  clock  when  it  is  desired 
to  give  it  a  uniform  motion  rather  than  to  record  the  speed  of  the  pulleys.  In 
practice  the  clock  and  recording  cylinder  have  been  used  as  the  registering  appa- 
ratus in  most  of  the  experiments  already  described  with  other  instruments. 

The  drawing  shows  a  portion  of  an  actual  dynamometer  trace  which  was 
obtained  with  the  instrument  when  set  in  motion  by  a  foot-lathe,  the  power 
supplied  by  the  foot  through  the  fly-wheel  of  the  lathe  being  transferred  by  a 
belt  to  the  pulley  and  thence  to  a  propeller  wheel  carried  at  the  end  of  the  shaft 
S.  The  pencil  P",  it  will  be  remembered,  is  connected  with  the  clock-spring,  its 
"  departure,"  or  motion  parallel  to  the  axis,  being  in  this  case  at  every  instant 
proportional  to  the  tension  at  the  same  instant  at  the  circumference  of  the  pulley. 
P'  is  the  pencil,  which  records  every  beat  of  the  mean  time-clock,  while  the  trace 
made  by  the  third  pencil,  P  (in  the  case  actually  under  consideration,  in  which 
the  dynamometer  is  at  rest),  measures  the  static  end-thrust  obtained  from  the 
propeller  blades  for  the  amount  of  power  put  out.  I  may  ask  attention  to  the 
comparability  of  these  two  absolutely  independent  traces,  and  invite  the  reader 
to  note  how  perfectly  the  relation  of  end-thrust  obtained  responds  to  the  power 
expended.  The  person  turning  the  lathe  did  so  with  the  greatest  uniformity 
attainable  by  the  use  of  a  heavy  fly-wheel,  but  every  motion  of  the  foot  is,  never- 
theless, as  will  be  seen,  most  conspicuously  registered.  Every  change  in  the 
amount  of  power  finds  also  its  counterpart  in  a  variation  of  end-thrust,  and  the 
inequalities  in  the  application  of  the  power  during  a  single  revolution  of  the  fly- 
wheel of  the  lathe  may  be  distinctly  traced  not  only  in  the  first  of  the  two  curves 
but  in  the  second.  (It  is  interesting  to  note  that  in  each  stroke  the  power  pen  P" 
starts  up  sharply  and  then  comes  nearly  or  quite  back  to  the  zero  line,  although 
we  see  from  the  pen  P  that  work  is  being  done  all  the  time.  This  is  repeated 
substantially  at  every  stroke  of  the  foot,  in  spite  of  the  inertia  of  the  lathe  fly- 
wheel, and  is  an  indication  of  the  extreme  sensitiveness  of  the  apparatus.) 

Preliminary  to  the  use  of  the  dynamometer  it  was  necessary,  as  has  been 
explained,  to  calibrate  the  clock-spring  and  the  end-thrust  spring  and  prepare 
curves  or  tables  for  evaluating  the  readings  of  the  traces. 

The  clock-spring  was  calibrated  in  the  following  manner:  The  propeller 
end  of  the  axle  being  held  fast,  weights  were  applied  at  the  circumference  of  the 
large  pulley,  10  centimeters  diameter,  by  means  of  a  cord.  The  torsional  force 


THE    DYNAMOMETER-CHRONOGRAPH. 


79 


of  these  weights  at  a  lever-arm  of  5  centimeters  (the  effective  radius  of  the  pulley) 
is  balanced  by  the  tension  of  the  clock-spring  and  is  measured  by  the  longitudinal 
motion  of  the  pencil  P".  On  account  of  the  appreciable  friction  of  the  guide- 
wheel  in  the  helical  groove,  two  measures  are  desirable  for  exact  calibration  in 
each  case  at  an  upper  and  lower  limit  of  repose.  The  mean  of  these  is  taken  as 
the  true  extension  for  the  given  weight,  and  the  observation  is  repeated  three 
times  with  each  weight  to  eliminate  errors  of  observation.  This  series  of  observa- 
tions was  made  with  the  set-screw  in  the  "0"  hole,  the  5th  hole,  and  the  10th 
hole,  in  order  to  get  a  sufficiently  wide  range  of  action  for  the  instrument 

The  following  table,  XVI,  gives  the  system  of  calibration  obtaitu  d  from 
experiments  made  November  14,  1890 — F.  W.  Very,  observer : 

TABLE  XVI. 
Calibration  of  Clock-Spring  of  Dynamometer. 

Weight  applied  at  circumference  of  large  pulley,  effective  radius  5 
centimeters,  by  cord  passing  over  a  small  pulley  at  edge  of  table. 


Position  of  set-screw. 

Weight. 

Extension  of  trace. 

Pounds. 

Grammes. 

Inches. 

Centimeters. 

10th  hole  

4.32 

1,960 

1.84 

4.67 

4.10 

1,860 

1.70 

4.32 

3.88 

1,760 

1.49 

3.77 

3.44 

1,560 

1.02 

2.59 

3.22 

1,460 

0.86 

2.18 

3.00 

1,360 

0.60 

1.52 

2.78 

1,260 

0.37 

0.94 

5th  hole  

300 

1  360 

1  89 

4  62 

2.78 

1J260 

I   -'   '_ 

1.60 

*XiVUl 

4.06 

2.56 

1,160 

1.35 

3.43 

2.34 

1,060 

1.15 

2.92 

2.12 

960 

0.88 

2.24 

1.90 

860 

0.66 

1.68 

1.68 

760 

0.41 

1.04 

"0"hole  

1  83 

830 

1.86 

473 

1.61 

730 

1.64 

Tt.  1  tJ 

4.17 

1.30 

630 

1.39 

3.53 

1.17 

530 

1.18 

3.01 

0.95 

430 

0.91 

2.31 

0.73 

330 

0.71 

1.79 

0.51 

230 

0.49 

1.24 

0.29 

130 

0.25 

0.63 

0.07 

30 

0.15 

0.38 

80 


EXPERIMENTS    IN    AERODYNAMICS. 


The  end-thrust  spring  was  calibrated  by  suspension  of  weights  in  a  similar 
way.  The  following  calibration  was  obtained  from  experiments  made  March  8, 
1888: 

Calibration  of  End-Thrust  Spring. 


Weight. 

Extension  of 
trace. 

(Grammes). 

(Centimeters). 

100 

0.43 

200 

1.07 

300 

1.75 

400 

2.21 

The  method  of  computing  the  horse-power  expended,  and  the  return  in  end- 
thrust  obtained,  may  now  be  illustrated  in  the  reduction  of  the  following  observa- 
tions taken  without  change  from  the  original  notes : 

* 

OCTOBER  30.  1888. 

Six-bladed  propeller,  with  blades  set  at  45°  with  axis.  Dynamometer  driven  by  belt  from  a 
small  dynamo.  Belt  driving  2.1  inch  pulley.  Dynamometer  geared  so  as  to  give  one  revolution 
of  cylinder  for  2,000  revolutions  of  pulley.  Time  of  one  revolution  of  cylinder,  295  seconds. 
Departure  of  pencil  of  clock-spring  (set-screw  in  "  0  "  hole),  1.43  inches. 

f»f\   .,    OfWVV 

Driving   pulley  makes       V.QK       revolutions  per  minute.     Circumference  of 

/yo 

2.1  x  3.1416  ,,  TT-  i     -4.      j?  u  i    60  x  2000  x  2.1  x  3.1416    ,, 

pulley  equals ^ fee*"     Velocity  of  belt  equals  -          295  x  12 

per  minute.  From  calibration  of  March  8,  1888,  an  extension  or  departure  of 
1.43  inches  of  the  pencil  of  the  clock-spring,  with  the  set-screw  in  "0"  hole, 
is  equivalent  to  a  weight  of  1.35  pounds  on  a  3.9-iiich  pulley.  The  tension  on 

the  present  2.1 -inch  driving  pulley  is  therefore  1.35  x  |^  pounds.     Multiplying 

tension  of  belt  by  velocity  of  belt  and  dividing  by  33,000,  we  have  the  work 
expended  per  minute  expressed  in  horse-power,  viz : 

60  X  2000  135  x  3.9  1.35 

X   3.1416  X       onnnn      =  3.713  X    ooc  =  0.017. 


295  x  12 


33000 


It  will  be  noticed  that  in  this  expression  the  factor  2.1  has  dropped  out,  and  the 
only  variables  are  the  time  of  one  revolution  of  cylinder  and  the  tension  on  the 
spiral  spring  taken  from  the  calibration  curve.  If  the  former  be  represented  by 
a  and  the  latter  by  b,  and  the  gearing  remain  unchanged,  the  horse-power  in  any 

experiment  will  be  given  by  the  formula  3.713  x  — 


THE    DYNAMOMETEH-CHKONOGRAPH.  81 

I  have  now  to  ask  attention  to  a  condition  of  vital  importance  in  the  experi- 
ments, and  yet  one  which  may,  perhaps,  not  appear  obvious.  It  is,  that  it  is 
indispensable  that  the  power  expended  on,  and  obtained  from,  the  propeller  shall, 
for  its  economical  use,  be  expended  on  fresh  and  undisturbed  masses  of  air.  To 
make  my  meaning  clearer,  I  will  suppose  that  the  Dynamometer -Chronograph  is 
mounted  On  a  fixed  support  in  the  open  air,  with  the  axis  pointing  east  and  west, 
and  that  in  a  perfect  calm  a  certain  amount  of  power  (let  us  suppose  n  horse- 
power) is  put  out  on  a  pulley  and  through  it  on  the  propeller,  giving  a  certain 
return  in  end-thrust.  Under  these  circumstances,  let  the  wind  blow  either  from 
north  to  south  or  from  south  to  north ;  that  is,  directly  at  right  angles  with  the 
axle,  so  that  it  might  at  first  sight  appear  that  nothing  is  done  to  increase  or 
diminish  the  amount  of  end-thrust  to  be  obtained.  The  amount  of  end-thrust 
under  these  circumstances  will,  in  fact,  be  very  greatly  increased  (even  though 
the  constant  expenditure  of  n  horse-power  be  maintained) — so  greatly  increased, 
that  a  neglect  of  such  considerations  would  completely  vitiate  the  results  of 
experiment,  the  great  difference  being  due  to  the  fact  that  the  propeller- wheel  is 
now  operating  from  moment  to  moment  on  fresh  masses  of  air  whose  inertia  has 
been  undisturbed. 

This  being  understood,  it  is  not  desirable  for  our  purpose  to  experiment 
upon  the  case  where  the  air  is  carried  at  right  angles  or  at  any  very  considerable 
angle  to  the  propeller  shaft — a  case  which  is  used  here  only  for  illustration  of  a 
principle.  The  circumstances  of  actual  motion  cause  the  wind  of  advance  to  be 
always  nearly  in  the  line  of  the  shaft  itself;  and  this  condition  is  obtained  by 
moving  the  instrument  so  that  the  wind  of  advance  caused  by  the  motion  of  the 
turn-table  is  in  this  direction.  It  is  this  supply  of  fresh  material  (so  to  speak) 
for  the  propeller  to  work  upon,  which  causes  the  need  of  noting  minutely  the 
speed  of  advance,  as  affecting  the  result,  so  that  for  a  given  constant  quantity  of 
power  expended,  the  percentage  of  return  in  end-thrust  depends  upon  the  rate 
of  supply  of  fresh  and  undisturbed  masses  of  air.  These  considerations  very 
intimately  connect  themselves  with  the  theory  of  the  marine  screw-propeller,  and 
the  related  questions  of  slip  and  rate  of  advance,  but  I  have  preferred  to  approach 
them  from  this  somewhat  less  familiar  point  of  view. 

The  dynamometer  and  propeller  were  therefore  mounted,  as  has  been  said, 
on  the  end  of  the  whirling-table.  The  propeller  was  driven  by  means  of  its 
pulley  C  by  a  belt  from  a  small  electro-motor  also  on  the  turn-table,  the  motor 
being  actuated  by  a  current  from  a  stationary  dynamo,  shown  on  plate  II.  This 
dynamo  sent  a  current  through  the  brush  contact  B  of  the  whirling-table  to  the 
small  electric  motor  mounted  on  the  arm.  The  whirling-table  was  then  raised 

11 


82  EXPERIMENTS    IN    AERODYNAMICS. 

out  of  its  gearings  by  the  means  shown  in  plate  II,  and  with  full  current  from 
the  dynamo  the  little  propeller  blades  proved  capable  of  rotating  the  great  turn- 
table, though  slowly,  for  manifestly  the  work  to  be  done  in  moving  this  great 
mass  was  quite  incommensurate  with  the  capacity  of  a  small  propeller  of  15  or  20 
inches  radius.  Some  special  means  must  therefore  be  devised  for  utilizing  the 
advantages  given  by  the  attainable  speed,  steadiness,  and  size  of  so  large  a 
whirling-table,  without  encountering  the  disadvantages  of  friction,  resistance  of 
the  air  to  the  exposed  surface,  and  similar  sources  of  difficulty.  To  place  the 
propeller  wheels,  either  actually  driving  inclined  planes  or  models,  or  otherwise, 
so  far  as  possible  under  the  conditions  they  would  have  in  actual  free  flight,  and 
to  measure  the  power  put  out  in  actuating  them,  the  resistance  experienced,  etc., 
under  these  conditions,  is  evidently  an  object  to  be  sought,  but  it  is  equally 
evident  that  it  is  difficult  of  attainment  in  practice.  Much  study  and  much 
experiment  were  given  to  this  part  of  the  problem,  with  the  result  of  the  inven- 
tion, or  rather  the  gradual  evolution  through  successive  forms,  of  the  auxiliary 
instrument  described  in  the  last  chapter  as  the  Component  Pressure  Recorder. 
This  conception  of  a  method  by  which  the  Dynamometer  could  be  effectively 
used  was  reached  in  February,  1889,  and,  together  with  its  final  mechanical 
embodiment,  was  the  outcome  of  much  more  thought  than  the  invention  of  the 
Dynamometer  itself. 

As  already  stated,  one  of  the  objects  of  the  Dynamometer  is  to  determine  the 
power  necessary  to  be  expended  in  mechanical  flight ;  but  manifestly  this  must  be 
done  indirectly,  for  we  have  to  experiment  with  a  model  or  an  inclined  plane  so 
small  as  to  be  incapable  of  soaring  while  supporting  the  relatively  great  weight  of 
the  Dynamometer-Chronograph,  even  if  it  had  an  internal  source  of  power  capable 
of  giving  independent  flight  (which  the  simple  inclined  plane  has  not).  If  such 
a  working  model  were  placed  upon  the  end  of  the  turn-table  arm,  with  the 
Dynamometer  supported  on  this  arm  behind  or  beneath  it,  and  if  the  arm  of  the 
turn-table  were  without  inertia  and  offered  no  resistance  to  the  air,  the  whole 
might  be  driven  forward  by  the  reaction  of  the  propeller  of  the  model,  actuated 
by  a  motor,  until  the  latter  actually  soars,  and  the  Dynamometer  supported  on 
such  an  imaginary  arm  might  note  the  work  done  when  the  soaring  takes  place. 
This  conception  is,  of  course,  impossible  of  realization,  but  it  suggests  a  method 
by  which  the  actual  massive  turn-table  can  be  used  so  as  to  accomplish  the  same 
result.  Suppose  the  model  with  attached  propeller  and  Dynamometer  to  be  placed 
on  the  end  of  the  whirling  arm,  and  the  latter  rotated  by  its  engine.  Further, 
suppose  the  model  aerodrome  be  also  independently  driven  forward  by  its  pro- 
peller, actuated  by  an  independent  motor,  at  the  same  speed  as  that  of  the  table ; 
then,  if  both  speeds  are  gradually  increased  until  actual  soaring  takes  place,  it  is 


THE    DYNAMOMETER-CHRONOGRAPH.  83 

evident  that  we  reach  the  desired  result  of  correct  dynamometric  measures  taken 
under  all  the  essential  circumstances  of  free  flight,  for  in  this  case  the  propeller  is 
driving  the  model  independently  of  any  help  from  the  turn-table,  which  latter 
serves  its  purpose  in  carrying  the  attached  Dynamometer. 

As  a  means  of  determining  when  the  propeller  is  driving  the  model  at  a 
speed  just  equal  to  that  of  the  turn-table,  let  the  whole  apparatus  on  the  end  of 
the  arm  be  placed  on  a  car  which  rolls  on  a  nearly  Motionless  track  at  right  , 
angles  to  the  turn-table  arm.  Then,  when  the  turn-table  is  in  rotation,  let  the 
propeller  of  the  model  be  driven  by  its  motor  with  increasing  speed  until  it 
begins  to  move  the  model  forward  on  the  track.  At  this  moment,  that  is,  just 
as  the  aerodrome  begins  to  move  forward  relatively  to  the  moving  turn-table, 
it  is  behaving  in  every  respect  with  regard  to  the  horizontal  resistance  (i.  e., 
the  resistance  to  advance),  as  if  it  were  entirely  free  from  the  table,  since  it  is 
not  moved  by  it,  but  is  actually  advancing  faster  than  it,  and  it  is  subject  in  this 
respect  to  no  disturbing  condition  except  the  resistance  of  the  air  to  the  bulk  of 
the  attached  Dynamometer.  In  another  respect,  however,  it  is  far  from  being 
free  from  the  table,  so  long  as  this  helps  to  take  part  in  the  vertical  resistance 
which  should  be  borne  wholly  by  the  air ;  the  aerodrome,  in  other  words,  will 
not  be  behaving  in  every  respect  as  if  in  free  air,  if  it  rests  with  any  weight  on 
the  track.  The  second  necessary  and  sufficient  condition  is,  then,  that  at  the 
same  moment  that  the  model  begins  to  run  forward  with  the  car  it  should  alse 
begin  to  rise  from  it.  This  condition  can  be  directly  obtained  by  rotating  the 
turn-table  at  the  soaring  speed  (previously  determined)  corresponding  to  any 
given  angle  of  the  inclined  plane. 

This  conception  of  a  method  for  attaining  the  manifold  objects  that  I  have 
outlined  was  not  carried  out  in  the  form  of  the  track,  which,  although  constructed, 
was  soon  abandoned  on  account  of  the  errors  introduced  by  friction,  etc.,  but  in 
the  Component  Recorder,  whose  freedom  of  motion  about  the  vertical  axis  provides 
the  same  opportunity  for  the  propeller  driven  model  to  run  ahead  of  the  turn- 
table as  is  offered  by  the  track.  This  instrument,  therefore,  a  part  of  whose 
functions  have  been  described  in  the  preceding  chapter,  has  been  used  as  a  neces- 
sary auxiliai*y  apparatus  to  the  Dynamometer -Chronograph,  and  this  is  an  essential 
part  of  the  purpose  for  which  it  was  originally  devised.  In  naming  the  instru- 
ment, however,  only  a  part  of  its  purpose  and  service  could  be  included,  or  of 
the  mechanical  difficulties  that  it  surmounts  indicated. 

The  investigation  of  the  velocity  at  which  an  inclined  plane  will  sustain  its 
own  weight  in  the  air,  and  the  determination  of  the  end-thrust,  or  horizontal 
resistance,  that  is  experienced  at  this  velocity,  were  made  with  the  Recorder 
independently  of  the  Dynamometer,  and  have  been  presented  in  detail  in  chapter 


84  EXPERIMENTS    IN    AERODYNAMICS. 

VI.  The  investigation  of  the  power  that  must  be  expended  to  furnish  this  end- 
thrust,  and  the  determination  of  the  best  form  and  size  of  propeller  for  the  pur- 
pose, combines  the  use  of  the  two  instruments. 

In  the  center  of  the  Recorder  is  provided  a  place  (see  plate  VII)  for  the 
electric  motor  already  referred  to,  whose  power  is  transmitted  by  a  belt  to  the 
pulley  of  the  Dynamometer-Chronograph,  which  is  mounted  on  the  end  of  the  rigid 
•  arms.  It  may  be  observed  that,  in  this  manner  of  establishing  the  motor,  the 
tension  of  the  pulley,  however  great,  in  no  way  interferes  with  the  freedom  of 
motion  of  the  arms  of  the  Recorder — a  very  essential  mechanical  condition,  and 
one  not  otherwise  easily  attainable.  With  the  various  pieces  of  apparatus  thus 
disposed,  and  with  the  propeller  to  be  tested  fastened  to  the  shaft  of  the  Dyna- 
mometer, the  whirling  table  is  rotated  at  any  desired  speed.  The  propeller  is  then 
driven  by  the  motor  with  increasing  amounts  of  power  until  the  forward  motion 
of  the  Recorder  arm  about  its  vertical  axis  indicates  that  the  propeller  is  driving 
the  Dynamometer  ahead  at  a  velocity  just  exceeding  the  velocity  of  the  whirling- 
table.  This  is  the  moment  at  which  all  the  records  admit  of  interpretation.  The 
work  that  is  being  done  by  the  propeller  is  that  of  overcoming  the  resistance  of 
the  air  to  the  bulk  of  the  Dynamometer,  and  in  place  of  this  we  may  substitute, 
in  thought,  the  resistance  that  would  be  caused  by  an  aerodrome  of  such  a  size 
as  to  produce  the  same  effect.  The  power  put  out  and  the  resistance  to  advance 
are  both  registered  on  the  cylinder  of  the  Dynamometer.  The  result  realized  is 
found  by  multiplying  the  static  pressure  indicated  by  the  pencil  which  registers 
the  end-thrust  by  the  velocity  of  the  turn-table  at  the  moment  when  the  pro- 
peller's independently  acquired  velocity  is  just  about  to  exceed  it.  The  static 
pressure  represents  the  resistance  overcome,  and  the  velocity  of  advance  gives 
the  distance  through  which  it  is  overcome  per  unit  of  time.  The  product  there- 
fore represents  the  effective  work  done  per  unit  of  time.  If  the  adopted  velocity 
of  the  whirling-table  be  the  soaring  velocity  of  an  aerodrome  which  would  have 
the  actually  observed  resistance,  the  experiment  will  virtually  be  made  under  all 
the  conditions  of  actual  horizontal  flight.  In  practice,  the  experiments  were 
made  at  a  series  of  velocities,  and  the  results  obtained — power  expended  and 
useful  work  done — can  be  interpolated  for  any  desired  speed. 

Preliminary  experiments  were  made  with  wooden  propellers  having  four, 
six,  and  eight  blades  set  at  different  angles  with  the  axis.  Lastly,  two  aluminum 
propellers  were  used  having  only  two  blades  each,  extending  24  and  30  inches, 
respectively,  from  tip  to  tip. 

In  order  that  the  reader  may  follow  the  method  of  experiment  in  detail,  the 
following  description  of  experiments  made  November  4,  1890,  is  here  given, 
together  with  abstracts  from  the  original  record  of  observations  for  that  date : 


THE    DYNAMOMETER-CHRONOGRAPH.  85 

NOVEMBER  4,  1890. 

Continuation  of  experiments  with  SO-inch  {diameter)  two-bladed  aluminum  propeller  to  determine  ratio 

of  power  put  out  to  return  in  end-thrust  obtained. 

Dynamometer-Chronograph  with  attached  propeller  is  placed  on  outer  arm  of  the  Component- 
Recorder  and  driven  by  an  electric  motor  placed  in  the  center  of  the  Recorder.  The  electric  motor 
is  run  by  a  dynamo,  the  current  from  which  is  carried  to  the  heavy  brush  contact  B  (plate  II)  of 
the  turn-table,  and  thence  along  the  arm  to  the  electric  motor,  and  the  dynamo  itself  is  run  by 
the  steam-engine  which  drives  the  turn-table. 

In  the  manner  already  described,  the  pencil  P"  of  the  Dynamometer-Chronograph  registers  the 
power  put  out;  P'  registers  seconds  from  the  mean  time-clock,  and  P  registers  the  end-thrust  of 
the  propeller.  A  fourth  pencil  is  fixed  to  the  frame  of  the  Recorder  and  registers  on  the  dyna- 
mometer cylinder  the  forward  motion  of  the  Recorder  arm  about  its  vertical  axis  against  the  ten- 
sion of  a  horizontal  spring,  the  spring  being  disposed  so  as  to  be  extended  by  the  forward  motion 
of  the  outer  arm.  Thus,  when  the  propeller  is  driven  at  such  a  velocity  as  just  to  exceed  the 
velocity  of  the  turn-table,  the  outer  arm  bearing  the  Dynamometer  moves  forward,  the  horizontal 
spring  begins  to  extend,  and  its  extension  is  recorded  on  the  Dynamometer  sheet,  together  with  the 
power  put  out,  the  amount  of  end-thrust  obtained,  and  the  time  trace  from  the  mean  time-clock. 

Preliminary  to  the  experiments  the  surface  of  the  inner  arm  of  the  balance  was  increased  so 
that  the  resistance  of  the  Dynamometer  on  the  outer  arm  to  the  wind  of  advance  should  be  largely 
counterbalanced.  This  was  accomplished  by  adding  a  surface  of  17  square  inches  at  a  distance 
of  4  inches  (104  centimeters)  from  the  axis  of  rotation. 

H.       YTi. 

At    2    12    Casella  air-meter  reads  1,779,600. 
At    5    39         "  "  "      1,881,900. 

Toward  end  of  experiments,  wind  almost  entirely  died  away. 

Dynamometer- Chronograph  sheet  No.  3 — notes  and  measurements : 

Propeller  blades  set  at  angle  of  75°  with  axis.    Horizontal  spring  No.  3. 

Pulley  cord  of  Dynamometer  running  on  4-inch  pulley. 

Chronograph  cylinder  geared  so  as  to  make  1  revolution  to  2,000  revolutions  of  propeller. 

Set  screw  of  Dynamometer  in  "  0  "  hole. 

Turn-table  driven  so  as  to  give  linear  speed  of  approximately  2,000  feet  per  minute. 

(a)  Dynamo  =  1,170  revolutions  per  minute. 

(6)  Propeller  =  5'52  *  2Q(-  =  1,032  revolutions  per  minute. 

(c)  Extension  of  power  pencil  P"  =  0.65  inches. 

(d)  Extension  of  end-thrust  pencil  P  =  0.20  inches  (varying). 

(e)  Horizontal  spring:  no  appreciable  extension,  except  occasional  jumps  produced  by  wind. 
(/)  Speed  of  turn-table  (from  sheet  of  stationary  chronograph  in  office)  =  5.41  seconds  in  one 

revolution  =  1,865  feet  per  minute. 

The  above  entries,  taken  from  the  original  note-book,  will  be  readily  under- 
stood in  connection  with  the  following  explanations : 

(a)  The  1,170  revolutions  of  dynamo  refer  to  the  revolutions  of  the  dynamo- 
electric  machine,  and  are  read  off  by  means  of  a  Buss-Sombart  Tachometer. 


86  EXPERIMENTS    IN    AERODYNAMICS. 

(ft)  5.52  is  the  number  of  inches  of  the  Dynamometer-Chronograph  barrel 
revolved  in  a  minute,  as  determined  by  measuring  the  time  trace.  An  entire 
revolution  corresponds  to  the  entire  circumference  of  the  barrel,  10.7  inches,  and 
(with  the  gearing  used  in  this  experiment)  to  2,000  revolutions  of  the  Dynamometer 
pulley  shaft. 

Hence 

5.52  x  2000 


10.7 


=  1,032 


is  the  number  of  revolutions  of  the  Dynamometer  pulley  per  minute  at  the  time 
of  this  experiment.  The  effective  diameter  of  the  pulley  being  4  inches,  this 
gives  for  the  velocity  of  the  cord  1,063  feet  per  minute. 

(c)  The  extension  of  the  power  pencil  P"  =  0.65  inches.  From  the  calibra- 
tion tables  we  find  that  this  corresponds  to  a  tension  of  0.67  pounds  on  the  pulley 
cord.  The  product  of  this  tension  by  the  pulley  speed  gives  the  power  put  out, 
viz.,  712  foot-pounds  per  minute. 

.(d)  The  extension  of  the  end-thrust  trace.  0.20  inch,  corresponds  to  a 
pressure  of  0  20  pound. 

(e)  The  horizontal  spring  has  no  appreciable  extension,  except  as  caused  by 
puffs  of  wind.     This  indicates  that  the  propeller  is  not  driving  quite  fast  enough 
to  equal  or  exceed  the  velocity  of  the  turn-table;  but  the  deficiency  of  velocity  is 
so  small  that  we  shall  not  discard  the  experiment,  but  compute  the  record  as  if 
the  requisite  velocity  were  just  attained. 

(f)  The  speed  of  turn-table  multiplied  by  the  end-thrust  gives  the  work 
done  per  minute  by  propeller,  viz.,  373  foot-pounds  per  minute. 

We  have,  then,  as  a  result  of  the  experiment,  that  the  ratio  of  work  done 
by  the  propeller  to  the  power  put  out  is  52  per  cent.,  the  form  of  the  propeller 
blades  not  being  a  very  good  one. 

The  whole  series  of  experiments  is  not  given  here  in  detail,  but  their  prin- 
cipal results  will  be  communicated  in  general  terms.  The  first  result  is  that  the 
maximum  efficiency  of  a  propeller  in  air,  as  well  as  in  water,  is  obtained  with  a 
small  number  of  blades.  A  propeller  with  two  blades  gave  nearly  or  quite  as 
good  results  as  one  with  a  greater  number.  This  is  strikingly  different  from  the 
form  of  the  most  efficient  wind-mill,  and  it  may  be  well  to  call  attention  to  the 
essential  difference  in  the  character  of  the  two  instruments,  and  to  the  fact  that 
the  wind-mill  and  the  movable  propeller  are  not  reversible  engines,  as  they  might 
at  first  sight  seem  to  be.  It  is  the  stationary  propeller — i.  <?.,  the  fan-blower— 
which  is  in  reality  the  reversed  wind-mill  ;  and  of  these  two,  the  most  efficient 
form  for  one  is  essentially  the  most  efficient  form  for  the  other.  The  efficiency 
of  a  fan-blower  of  given  radius  is  expressed  in  terms  of  the  quantity  of  air 
delivered  in  a  unit  of  time  for  one  unit  of  power  put  out ;  that  of  the  wind- mill 


THE   DYNAMOMETER-CHRONOGRAPH.  87 

may  be  expressed  in  terms  of  the  amount  of  work  done  per  unit  quantity  of  air 
passing  within  the  radius  of  the  arms.  If  any  air  passes  within  the  perimeter 
which  does  not  strike  the  arms  and  do  its  work,  it  is  so  much  loss  of  an  attainable 
efficiency.  This  practical  conclusion  is  confirmed  by  experience,  since  modern 
American  wind-mills,  in  which  practically  the  entire  projection  area  is  covered 
with  the  blades,  are  well  known  to  be  more  efficient  than  the  old  wind-mills  of 
four  arms. 

Turning  now  to  the  propeller,  it  will  be  seen  that  the  expression  for  its 
efficiency,  viz.,  the  ratio  of  useful  work  done  to  power  expended,  involves  quite 
different  elements.  Here  the  useful  work  done  (in  a  unit  of  time)  is  the  product 
of  the  resistance  encountered  by  the  distance  advanced,  which  is  entirely  different 
in  character  from  that  in  the  fan-blower,  and  almost  opposite  conditions  conduce 
to  efficiency.  Instead  of  aiming  to  set  in  motion  the  greatest  amount  of  air,  as 
in  the  case  of  the  fan-blower,  the  most  efficient  propeller  is  that  which  sets  in 
motion  the  least.  The  difference  represents  the  difference  between  the  screw 
working  in  the  fluid  without  moving  it  at  all,  as  in  a  solid  nut,  and  actually 
setting  it  in  motion  and  driving  it  backward — a  difference  analogous  to  that  which 
in  marine  practice  is  technically  called  "  slip,"  and  which  is  a  part  of  the  total 
loss  of  efficiency,  since  the  object  of  the  propeller  is  to  drive  itself  forward  and 
not  to  drive  the  air  backward.  It  may  now  be  seen  why  the  propeller  with  few 
blades  is  more  efficient  than  one  with  many.  The  numerous  blades,  following 
after  each  other  quickly,  meet  air  whose  inertia  has  already  yielded  to  the  blades 
in  advance,  and  hence  that  does  not  offer  the  same  resistance  as  undisturbed  air 
or  afford  the  same  forward  thrust.  In  the  case  of  the  propeller  with  two  blades, 
each  blade  constantly  glides  upon  new  strata  of  air  and  derives  from  the  inertia 
of  this  fresh  air  the  maximum  forward  thrust.  The  reader  will  observe  the 
analogy  here  to  the  primary  illustration  of  the  single  rapid  skater  upon  thin  ice, 
who  advances  in  safety  where  a  line  of  skaters,  one  behind  the  other,  would 
altogether  sink,  because  he  utilizes  all  the  sustaining  power  to  be  derived  from 
the  inertia  of  the  ice  and  leaves  only  a  sinking  foothold  for  his  successors.  The 
analogy  is  not  complete,  owing  to  the  actual  elasticity  of  air  and  for  other  reasons, 
but  the  principle  is  the  same.  A  second  observation  relating  to  aerial  propellers, 
and  one  nearly  related  to  the  first,  is  that  the  higher  the  velocity  of  advance 
attained,  the  less  is  the  percentage  of  "  slip,"  and  hence  the  higher  the  efficiency 
of  the  propeller.  The  propeller  of  maximum  efficiency  is  in  theory  one  that 
glides  through  the  air  like  a  screw  in  an  unyielding  frictionless  bearing,  and 
obtains  a  reaction  without  setting  the  air  in  motion  at  all.  Now,  a  reaction  from 
the  air  arising  from  its  inertia  increases,  in  some  ratio  as  yet  undetermined,  with 
the  velocity  with  which  it  is  struck,  and  if  the  velocity  is  high  enough  it  is 
rendered  probable,  by  facts  not  here  recorded,  that  the  reaction  of  this  ordinarily 


88  EXPERIMENTS    TN    AERODYNAMICS. 

most  mobile  gas  may  be  practically  as  great  as  we  please  and,  with  explosive 
velocities,  for  instance,  may  be  as  great  as  would  be  the  reaction  of  a  mass  of  iron. 
The  theory  of  aerial  propellers  being  that  for  a  maximum  efficiency,  the 
higher  the  velocity,  the  sharper  should  be  the  pitch  of  the  blades,  it  has  been  tin- 
object  of  the  complete  series  of  experiments  with  the  Dynamometer-Chronograph 
to  determine  by  actual  trial  the  velocity  of  advance  at  which  the  maximum 
efficiency  is  attained  when  the  blades  are  set  at  different  angles,  and  the  best 
forms  and  dimensions  of  the  blades.  The  details  of  these  are  reserved  for  future 
publication,  but,  very  generally  speaking,  it  may  be  said  that  notwithstanding 
the  great  difference  between  the  character  of  the  media,  one  being  a  light  and 
very  compressible,  the  other  a  dense  and  very  incompressible  fluid,  these  observa- 
tions have  indicated  that  there  is  a  very  considerable  analogy  between  the  best 
form  of  aerial  and  of  marine  propeller. 


CHAPTER   VIII. 
THE  COUNTERPOISED   ECCENTRIC   PLANE. 

If  a  rectangular  plane  be  made  to  move  through  the  air  at  an  angle  of 
inclination  with  the  direction  of  advance,  it  was  implicitly  assumed  by  Newton 
that  the  center  of  pressure  would  coincide  with  the  center  of  figure.  Such,  how- 
ever, is  not  the  case,  the  pressure  being  always  greater  on  the  forward  portion, 
and  the  center  of  pressure  varying  with  the  angle  of  inclination. 

The  object  of  the  present  chapter  is  to  present  the  results  of  experiments 
made  to  determine  the  varying  positions  of  the  center  of  pressure  for  varying 
angles  of  inclination  of  a  plane  moved  in  a  horizontal  course  through  the  air. 
Drawings  of  the  apparatus  devised  for  this  purpose  are  given  on  plate  V.  A  A' 
represents  the  eccentric  wind-plane  one  foot  square  held  in  a  brass  frame  about 
4  of  an  inch  wide  and  I  of  an  inch  thick.  Two  sliding  pieces,  SS',  move  in  a 
groove  in  the  edge  of  the  brass  frame,  and  may  be  clamped  in  any  position  by 
screws.  Each  sliding  piece  has  a  small  central  hole,  in  which  fits  a  pivot.  V. 
The  wind-plane  (eccentric  plane)  is  suspended  by  these  pivots  and  swings  about 
the  axis  passing  through  them,  so  that  by  moving  the  plane  in  the  sliding 
pieces  this  axis  of  rotation  can  be  moved  to  any  distance  up  to  two  inches.-  A 
flat  lead  weight,  which  also  slides  along  the  back  of  the  plane,  can  be  adjusted 
so  as  to  counterpoise  it  in  any  position.  When  the  weight  is  adjusted,  therefore, 
the  plane  is  in  neutral  equilibrium  about  its  axis  of  rotation.  A  pencil,  P,  is 
fixed  on  the  lower  part  of  the  plane  and  records  against  a  tracing  board  perpen- 
dicular to  it.  In  order  to  leave  the  position  of  the  plane  entirely  uncontrolled 
by  the  friction  of  the  pencil,  the  registering  board  is  held  away  from  the  plane 
by  spring  hinges  HH',  and  caused  to  vibrate  by  an  electro-magnet  so  as  to  touch 
the  pencil  point  many  times  in  a  second. 

In  the  experiments  the  sliding  pieces  were  set  so  that  the  axis  of  rotation 
was  successively  0  inch,  0.25  inch,  0.75  inch,  etc.,  from  the  center,  and  the 
plane  was  counterpoised  about  this  axis.  When  placed  in  rotation  upon  the  arm 
of  the  whirling-table,  the  moment  of  rotation  of  the  plane  about  the  axis  is  pro- 
portional to  the  resultant  wind  pressure  multiplied  by  the  distance  of  the  center 
of  pressure  from  the  axis  of  rotation,  and  it  will  reach  its  position  of  equilibrium 
when  the  plane  has  taken  up  such  an  angle  of  inclination  that  the  center  of 

12  I8ff\ 


.90 


EXPERIMENTS    IN    AERODYNAMICS. 


pressure  is  at  the  axis  of  rotation.  The  measurement  of  this  angle  is,  therefore, 
the  object  of  observation. 

In  actual  experiment  the  exact  angle  of  equilibrium  of  the  plane  is  masked 
by  slight  inequalities  of  speed  and  by  fluctuation  of  the  vincl,  and  there  is  oscil- 
lation about  a  mean  position.  In  measuring  the  trace,  the  extreme  angles  of  this 
oscillation  were  read,  as  well  as  the  mean  position  of  equilibrium. 

The  following  transcript  from  the  note-book  for  September  22.  1888,  will 
afford  an  illustration  of  the  detailed  records  made  in  connection  with  each  series 
of  experiments.  The  column  headed  "  range  "  gives  the  range  of  oscillation  of 
the  plane,  and  shows  that  the  plane  is  far  more  unsteady  when  the  axis  of  oscil- 
lation and  center  of  pressure  is  very  eccentric  than  wnen  it  is  nearer  the  center. 

SEPTEMBER  22,  1888. 


Time. 

Barometer. 
(Inches.) 

Air  tempera- 
ture, 
(lahr.) 

Wind  diree- 
ti>n. 

Air  meter. 

10.20  a.  m. 
12.20  a.  in. 

29.080 
29.069 

6S& 

61.2 

N.  N.  E. 
N.  A',  t. 

183380 
224065 

Meteorological  conditions  not  so  favorable  as  yesterday,  the  wind  being  rather  strong. 

Engine  run  by  Eis!«r ;  J.  Ludewig  sets  wind-plane ;  F.  W.  Very  attends  to  chronograph  and  records. 


t»   m 

**-»  d  o 

fl 

V- 

O  <K 

o 

*L 

00    O    3 

•5 

J 

'§!•§ 

"  EC 

ii 

ro5 

Time. 

1    ° 

°%°  % 

•"'•£ 

o  £ 

Range. 

h  °  & 

0^5  o^; 

"o  ^ 

I* 

C"ftft 

I  fell 

w  o  o  -^ 

V   " 

"5c 

I 

X 

M 

p 

<5 

W 

0         0 

0 

10.38  a.  m. 

12.8 

2.00 

82.0 

64-98 

34 

10.42  a.  m. 

12.8 

1.75 

76.0 

58-98 

40 

10.46  a.  m. 

12.8 

1.75 

76.0 

10.50  a.  m. 

12.9 

1.50 

68.0 

48-84 

36 

12.12  p.  in. 

13.3 

0.00 

6.0 

0.12 

12 

Two  complete  sets  of  observations  were  made,  both  on  September  21  and 
September  22,  1888,  making  in  all  31  separate  readings,  which  are  given  in  detail 
at  the  close  of  the  chapter. 

The  mean  of  these  observations  is  presented  in  the  following  table  XVII : 


THE   COUNTERPOISED    ECCENTRIC   PLANE. 


91 


TABLE  XVII. 

Sumrruiry  of  Experiments  giving  position  of  center  of  pressure  on  a  plane  one  foot  square  (30,5  x  30.5 

centimeters)  for  different  angles  of  inclination. 


Distance  from  center  of  press- 
ure to  center  of  plane  d. 

Distance    as    a 
percentage  of 
the  side  of  the 

Angle  of  trace 
with  initial 

Angle  of  plane 
with 
vertical 

Angle  of  plane 
with 
horizontal 

(Inches.) 

(Centimeters.) 

plane. 

line. 

90°  -  «. 

a. 

o 

o 

0.00 

0.00 

0.000 

5.5 

0.0 

90.0 

0.25 

0.64 

0.021 

17.4 

12.0 

78.0 

0.50 

1.27 

0.042 

28.2 

22.7 

67.3 

0.75 

1.90 

0.063 

39.7 

34.2 

55.8 

1.00 

2.54 

0.083 

50.6 

45.0 

45.0 

1.25 

3.17 

0.104 

59.7 

54.2 

35.8 

1.50 

3.81 

0.125 

67.5 

62.0 

28.0 

1.75 

4.44 

0.146 

75.0 

69.5 

20.5 

The  first  two  columns  give  the  distance  from  the  center  of  pressure  to  the  center 
of  the  plane  in  centimeters  and  inches,  and  the  third  column  gives  it  as  a  per- 
centage of  the  length  of  the  plane.  The  fourth  column  gives  the  angle  of  trace 
with  the  initial  vertical  line  drawn  through  the  position  of  the  pencil  at  rest.  It 
will  be  noticed  that  this  angle  is  5°.5  for  the  case  when  the  axis  of  rotation  passes 
through  the  center  of  the  plane — a  setting  for  which  the  plane  must  be  vertical. 
This  observed  angle  of  5° .5  is  to  be  explained,  not  by  a  tipping  of  the  plane, 
but  by  a  tipping  of  the  line  of  reference  due  to  a  yielding  of  the  supports,  etc.,  to 
the  wind  of  rotation.  This  angular  deflection,  therefore,  becomes  a  correction  to 
be  applied  to  all  the  observations,  and  the  fifth  column,  headed  "  angle  of  plane 
with  vertical,"  contains  the  corrected  values  for  the  inclination  of  the  plane. 

The  resulting  relations  here  established  between  the  angle  of  inclination  of 
the  plane  and  the  position  of  the  center  of  pressure  are  of  importance,  but  their 
application  is  not  made  in  the  present  memoir.* 


*  References  to  the  results  of  Joessel  and  of  Kummer  will  be  found  in  Appendix  C. 


92 


EXPERIMENTS    IN    AERODYNAMICS. 


Experiments  to  determine  the  position  of  the  center  of  pressure  on  an  inclined  square  plane. 

SEPTEMBER  21,  1888. 
F.  W.  VERY,  Conducting  experiments;  JOSEPH  LUDEWIG,  Assisting. 

Barometer,  737.06  mm. ;  temperature,  18°  C. ;  wind  velocity,  0.006  meter  per  second  ;  length 
of  side  of  wind-plane,  12  inches  (30.5  centimeters). 


•8J 

Distance  of  axis  of  oscil- 

g 

'o 

£*£ 

lation    from    center   of 

<fc! 

' 

•§! 

plane. 

S    O 

To  . 

Time. 

"l^p. 

o  * 

Range. 

I-,^^ 

*O    <D 

a* 

a?  °s  o 

J  "5,1 

(Inches.) 

(Centimeters.) 

f 

1 

p.  in. 

O 

o      o 

o 

3.17 

4.49 

1.75 

4.44 

76.0 

65-88 

23 

3.23 

4.49 

1.50 

3.81 

67.5 

60-75 

15 

3.28 

4.49 

1.25 

3.17 

60.0 

57-63 

G 

3.33 

4.51 

1.00 

2.54 

50.4 

47-54 

7 

3.37 

4.47 

0.75 

1.90 

39.0 

87-41 

4 

3.41 

4.51 

0.50 

1.27 

29.5 

29-30 

1 

3.45 

4.46 

0.25 

0.64 

20.9 

19-23 

4 

3.48 

4.49 

0.00 

0.00 

6.4 

2-11 

9 

3.58 

8.47 

1.75 

4.44 

73.0 

61-91 

30 

4.02 

8.57 

1.50 

3.81 

67.0 

50-80 

30 

4.06 

8.70 

1.25 

3.17 

60.0 

58-63 

5 

4.09 

8.56 

1.00 

2.54 

50.5 

47-55 

8 

4.25 

7.92 

0.75 

1.90 

40.1 

37-43 

6 

4.34 

8.47 

0.50 

1.27 

28.5 

28-31 

2 

4.41 

7.81 

0.25 

0.64 

16.3 

15-17 

2 

4.44 

7.63 

0.00 

0.00 

5.0 

4-7 

3 

THE    COUNTERPOISED    ECCENTRIC    PLANE. 


93 


SEPTEMBER  22,  1888. 

F.  W.  VERY,  Conducting  experiments;  JOSEPH  LUDEWIG,  Assisting. 
Barometer,  738.4  nrau ;  temperature,  15.°5  0. ;  wind  velocity,  2.06  meters  per  second. 

Meteorological  conditions  not  so  favorable  as  on  the  21st,  the  wind  being  rather  strong.     The 
effect  is  to  produce  a  much  wider  oscillation  of  the  trace. 


"o  S3 

ft 

Distance  of  axis  of  oscil- 

I 

<H 

O 

,5*  £ 

lation   from    center   of 

Cl 

r^ 

11 

plane. 

I'd 

fl 

Time. 

1>    S--4. 

•fi 

«   «3 

Range. 

I'ai 

(Inches.) 

(Centimeters.) 

"SB 
q 

1 

X 

r-3 

W 

a.  m. 

o 

O         O 

o 

10.38 

12.8 

2.00 

5.08 

82.0 

64-98 

34 

10.42 

12.8 

1.75 

4.44 

76.0 

58-98 

40 

10.46 

12.8 

1.75 

4.44 

76.0 

10.50 

12.9 

1.50 

3.81 

68.0 

48-84 

36 

10.55 

10.4 

1.25 

3.17 

59.0 

35-76 

41 

11.26 

13.6 

1.00 

2.54 

51.0 

37-59 

22 

11.29 

13.6 

0.75 

1.90 

40.0 

37-43 

6 

11.32 

14.3 

0.50 

1.27 

26.5 

25-28 

3 

11.36 

13.4 

0.25 

0.64 

15.0 

11-19 

8 

11.41 

13.8 

0.00 

0.00 

5.0 

3-7 

4 

11.58 

14.5 

2.00 

5.08 

79.0 

58-96 

38 

p.  m. 

12.03 

14.7 

1.50 

3.81 

66.0 

50-80 

30 

12.06 

14.0 

1.00 

2.54 

49.0 

45-52 

7 

12.09 

13.8 

0.50 

1.27 

27.0 

26-28 

2 

12.12 

13.3 

0.00 

0.00 

6.0 

0-12 

12 

Note  to  Second  Edition.  The  extreme  forward  position  of  the  centre  of  pressure  in  these  experiments 
was  for  the  smallest  angle,  one-fourth  the  length  of  the  plane  from  the  front  edge,  but  subsequent  experiments, 
at  Washington,  with  lighter  planes  have  shown  that  it  may  be  as  little  as  one-sixth  or  even  less.  Moreover, 
it  appears  probable,  though  it  is  not  demonstrated,  that  for  an  increased  speed  this  centre  of  pressure  tends 
to  move  forward  even  when  there  is  no  proposed  diminution  of  the  angle  with  the  horizontal. 


CHAPTER  IX. 

THE  ROLLING  CARRIAGE. 

The  Boiling  Carriage  was  constructed  for  the  purpose  of  determining  the 
pressure  of  the  air  on  a  plane  moving  normal  to  its  direction  of  advance.*  What- 
ever be  the  importance  of  this  subject  to  aerodynamics  or  engineering,  we  are 
here  interested  in  it  only  in  its  direct  bearing  on  the  aerodromic  problem,  and 
carry  these  observations  only  as  far  as  this  special  object  demands.  Before  this 
instrument  was  constructed,  a  few  results  had  already  been  obtained  with  the 
Resultant  Pressure  Recorder  (chapter  IV),  but  additional  observations  were  desired 
with  an  instrument  that  would  be  susceptible  of  greater  precision.  The  state- 
ment has  frequently  been  made  that  the  law  that  the  pressure  is  proportional  to 
the  square  of  the  velocity  fails  for  low  velocities  as  well  as  for  very  high  ones. 
As  it  appears  to  me  that  this  conclusion  was  probably  based  on  imperfect  instru- 
mental conditions  due  to  the  relatively  excessive  influence  of  the  friction  of  the 
apparatus  at  low  velocities,  particular  pains  were  taken  in  the  present  experi- 
ments to  get  as  frictionless  an  action  as  possible.  Plates  IX  and  X  contain 
drawings  in  elevation  and  plan  of  the  apparatus  devised  for  this  purpose. 

A  metal  carriage  8i  inches  long  is  suspended  on  a  set  of  delicately  con- 
structed brass  wheels  5  inches  in  diameter,  which  roll  on  planed  ways.  Friction 
wheels  bearing  against  the  sides  and  bottom  of  the  planed  ways  serve  as  guides 
to  keep  the  carriage  on  its  track.  Cushions  of  rubber  at  each  end  break  the 
force  of  any  end-thrust.  Through  the  center  of  this  carriage  passes  a  hollow 
brass  rod  27i  inches  long,  on  the  forward  end  of  which  is  set  the  wind-plane  by 
means  of  a  socket  at  its  center.  On  the  other  end  is  attached  a  spiral  spring, 
which  is  also  fastened  by  a  hook  to  the  rear  of  the  carriage-track  in  a  manner 
illustrated  in  the  drawing.  The  rod  is  of  such  length  that  the  wind-plane  may 
be  removed  from  the  disturbing  influence  on  the  air  of  the  mass  of  the  registering 
apparatus,  and  the  center  of  gravity  of  wind-plane  and  rod  falls  under  the  center 
of  gravity  of  the  carriage.  The  pressure  of  the  wind  on  the  wind-plane  is  bal- 

*  These  measurements  of  pressure  on  the  normal  plane  are  not  presented  as  new.  They  were  made  as  a 
necessary  part  of  an  experimental  investigation  which  aimed  to  take  nothing  on  trust,  or  on  authority  however 
respectable,  without  verification.  They  are  in  one  sense  supplementary  to  the  others,  and  although  made  early 
in  the  course  of  the  investigations  presented  in  this  memoir,  are  here  placed  last,  so  as  not  to  interrupt  the 
presentation  of  the  newer  experiments,  which  are  related  to  each  other  by  a  consecutive  development. 

(94> 


THE    ROLLING   CARRIAGE. 


95 


anced  by  the  extension  of  the  spiral  spring,  while  the  Boiling  Carriage  bears  an 
arm,  F,  carrying  a  pencil  which  rests  upon  a  chronograph  cylinder  to  automat- 
ically record  this  pressure,  the  axis  of  the  cylinder  being  parallel  to  the  track  of 
the  carriage  and  the  chronograph  rotated  by  clock-work.  The  position  of  the 
pencil  for  zero  pressure  on  the  spring  is  marked  on  the  chronograph  sheet,  and 
a  reference  line  is  drawn  through  this  point,  so  that  distances  of  the  pencil  point 
from  this  reference  line  are  measures  of  the  extension  of  the  spring,  while  a  second 
pencil,  being  placed  on  the  opposite  side  of  the  chronograph  barrel,  and  operated 
by  an  electro-magnet  in  electrical  connection  with  the  mean  time  clock,  registers 
seconds  on  the  chronograph  barrel,  and  thereby  every  point  of  the  pressure  trace 
made  by  the  first  pencil  can  be  identified  with  the  synchronous  points  in  the 
trace  on  the  stationary  chronograph  on  which  is  registered  the  velocity  of  the 
whirling-table. 

Much  care  was  bestowed  upon  the  manufacture  and  calibration  of  the  spiral 
springs.  The  following  is  a  list  of  the  springs,  giving  their  size,  length,  and 
weight : 


d 

_H 

^ 

o^ 

^ 

'o 

o 

GO 

0 

!_,     ttD 

PQ  g 

B 
J 

O    CD 

§ 

V  ^o 

O 

0) 

I 

§5 

"3 

If 

^ 

jg    g 

-3S 

.fl 

•g 

t«  J5 

« 

®    V^/ 

<~] 

a 

B 

0> 

-s 

§2 

(JJ 

1 

'S 

fc 

s 

to 

p 

^ 

1 

Steel  . 

52 

4.5 

0.75 

64 

2 

Brass. 

60 

5.0 

0.30 

18 

3 

Steel  . 

56 

5.6 

0.60 

43 

4 

Steel  . 

51 

5.7 

0.65 

71 

7 

Steel  . 

42 

6.0 

0.80 

128 

The  method  of  calibration  adopted  is  as  follows : 

The  spring  to  be  calibrated  is  fastened  at  one  end  to  the  brass  tube  of  the 
Soiling  Carriage  and  at  the  other  to  a  fixed  support.  A  string  fastened  to  the  end 
of  the  shaft  passes  over  a  light,  almost  frictionless  pulley,  and  carries  a  bag,  in 
which  the  weights  are  placed.  The  extensions  of  the  spring  are  registered  by 
the  pencil  on  the  chronograph  barrel.  Settings  are  made  on  opposite  sides  of  a 
mean  position,  first,  by  letting  the  weight  fall  gradually  to  its  lowest  position ; 
and,  second,  by  extending  it  beyond  its  normal  position  and  allowing  the  tension 
of  the  spring  to  draw  it  back.  In  both  cases  a  series  of  vibrations  are  sent 
through  the  apparatus  by  the  jar  set  up  on  the  table,  by  means  of  a  large  tuning- 
fork,  so  as  to  overcome  the  friction  of  the  moving  parts.  In  a  portion  of  the 
calibration  experiments,  these  vibrations  were  produced  by  an  electro- magnet. 


96  EXPERIMENTS    IN    AERODYNAMICS. 

The  results  of  the  calibration  were  plotted  in  curves,  and  these  curves  have 
been  used  for  translating  all  the  spring  extensions  of  the  experiments  into 
pressures. 

Three  square  planes  were  used,  6,  8,  and  12  inches  on  a  side,  and  in  every 
case  the  center  of  the  plane  was  placed  nine  meters  from  the  center  of  the 
whirling-table.  The  air  temperature  was  recorded  at  the  beginning  and  end 
of  each  series  of  observations.  The  average  wind  velocity  was  obtained  from  a 
Casella  air  meter,  which  was  read  each  day  at  the  beginning  and  end  of  the 
experiments.  It  should  be  noted  that  these  wind  velocities  are  valuable  as  indi- 
cating the  conditions  of  experiment,  but  do  not  afford  any  basis  of  correction  to 
the  observations,  since  the  method  adopted  in  reading  the  trace  eliminates  the 
effect  of  wind  currents,  so  far  as  it  is  possible  to  do  so.  In  a  complete  revolution 
of  the  turn-table  the  arm  during  half  of  the  revolution  moves  with  the  wind,  and 
during  the  other  half  moves  against  the  wind;  consequently  the  pressure  will 
be  too  great  during  the  latter  half  and  too  small  during  the  former  half  of  the 
revolution.  Thus,  if  the  velocity  at  the  end  of  the  arm  be  F,  and  the  wind 
velocity  be  u,  the  wind  pressure  at  one  point  of  the  revolution  will  be  propor- 
tional to  ( V+  v)2,  and  at  the  opposite  point  will  be  proportional  to  (  V—  v)1.  The 
resulting  trace,  therefore,  vibrates  on  either  side  of  a  mean  position,  and  a  line 
drawn  through  the  trace  to  represent  this  mean  position  gives  a  numerical  value 
that  is  larger  than  the  pressure  due  to  the  velocity  V  in  the  ratio  of  FJ  +  v2  to  V~. 
But,  in  general,  this  error  in  reading  the  traces  is  quite  negligible,  and  the  average 
mean  position  may  be  taken  as  reliable  within  the  limits  of  accuracy  imposed 
on  us.  The  spring  extension  adopted  always  refers  to  this  mean  position,  and  no 
further  correction  is  admissible.  A  specimen  of  the  records  of  a  series  of  experi- 
ments is  here  given  in  detail,  taken  from  the  note  book  for  October  25,  1888: 

OCTOBER  25,  1888. 

Barometer,  738  mm. ;  mean  temperature,  16°  C.  At  4.53  p.  m.,  air  meter,  416,445  ;  at  5.25 
p.  m.,  air  meter.  419,130.  Eight-inch  square  wind-plane.  Spring  No.  1.  Distance  of  center  of 
plane  from  axis  of  rotation,  9  meters. 

First  registering  sheet.  Four  records  at  about  4J  revolutions  per  minute.  Ended  at  4.05. 
Almost  a  perfect  calm.  Velocity  too  small  to  get  reliable  spring  extensions. 

Second  sheet  started  at  4.24  p.  m.  Two  records  at  10  revolutions  per  minute.  Ended  at 
4.28  p.  m.  Pencil  failed  to  make  satisfactory  record. 


THE    ROLLING   CARRIAGE. 


97 


Third  sheet  started  at  4.34  p.  m.  at  nearly  14  revolutions  per  minute.     Four  records  obtained. 

Ended  at  4.44  p.  m. 

Reading  of  traces. 


Number  of  seconds 
in  one  revolution 
of  turn-table. 

Velocity  of  center  of 
plane  (meters  per 
second). 

Extension  of  spring 
No.  1  (inches). 

Pressure    on    plane 
(pounds). 

4.29 
4.29 
4.38 
4.38 

13.14 
13.14 
12.93 
12.93 

0.97 
0.75 
0.82 
0.78 

1.30 
1.10 
1.15 
1.12 

Fourth  sheet.     Velocity  about  20  revolutions  per  minute.     Two  records  obtained.     Ended 

at  4.57  p.  m. 

Reading  of  traces. 


Number  of  seconds 
in  one  revolution 
of  turn-table. 

Velocity  of  center  of 
plane  (meters  per 
second). 

Extension  of  spring 
No.  1  (inches). 

Pressure    on    plane 
(pounds). 

2.88 
2.90 

19.60 
19.50 

2.33 
2.28 

2.55 
2.51 

Fifth  sheet.     Velocity  about  25  revolutions  per  minute.     Two  records  obtained.     The  first 
record  is  good.     The  second  record  cannot  be  interpreted.     Ended  at  at  5.15  p.  m. 

Reading  of  traces. 


Number  of  seconds 
in  one  revolution 
of  turn-table. 

Velocity  of  center  of 
plane  1  meters  per 
second). 

Extension  of  spring 
No.  1  (inches). 

Pressure    on    plane 
(pounds). 

2.45 

23.10 

3.76 

3.90 

The  experiments  were  made  from  October  24  to  November  2,  1888,  with  a 
short  series  on  November  28,  1890,  and  embrace  observations  with  6,  8,  and  12 
inch  square  planes,  those  with  the  6-inch  plane  extending  over  velocities  from  7 
to  30  meters  per  second.  They  are  presented  in  extenso  at  the  end  of  the  present 
chapter  The  extension  of  the  spring  is  given  in  inches,  as  originally  measured 
from  the  trace,  and  the  corresponding  pressures  are  given  in  pounds  and 
grammes.  The  next  succeeding  column  gives  the  pressure  P  in  grammes  per 
square  centimeter  of  the  wind-plane  sin-face.  The  last  column  gives  the  value  of 
the  coefficient  km  in  the  equation  P  =  km  V'-,  where  P  is  the  pressure  in  grammes 
on  a  square  centimeter  of  surface,  and  Fthe  velocity  expressed  in  meters  per 
second.  The  subscript  m  is  used  here,  as  in  previous  chapters,  to  designate  these 
metric  units. 

One  of  the  objects  of  the  experiments  was  to  test  the  generally  accepted  law, 
that  the  pressure  varies  as  the  square  of  the  velocity,  and  for  this  purpose 

13 


98 


EXPEKIMRNTS    IN    AERODYNAMICS. 


velocities  were  used  ranging  from  7  to  30  meters  per  second  (11  to  67  miles  per 
hour).  The  mean  of  10  observations  with  the  6-inch  plane,  at  velocities  between 
25  and  30  meters  per  second,  gave  km  =  0.0081 ;  and  the  mean  of  12  observations, 
at  velocities  between  7.1  and  14.3  meters  per  second,  gave  the  same  value. 
Therefore  the  departure  from  the  law  of  the  squares,  if  there  be  any  between 
these  limits  of  velocity,  is  not  sufficiently  large  to  be  detected  by  this  apparatus. 
If  variations  in  the  density  of  the  air  produced  by  changes  of  temperature 
be  considered  in  their  effect  upon  the  relation  between  pressure  and  velocity,  the 
preceding  formula  may  be  expressed  in  the  form 

p  _  kmV* 

1  +  .00366  (t  —  10°)' 

where  .00366  is  the  coefficient  of  expansion  of  air  per  centigrade  degree ;  t  is  the 
temperature  of  the  air  expressed  in  centigrade  degrees,  and  km  is  the  value  of 
the  coefficient  for  a  standard  temperature  of  10°  C.  In  the  following  summary, 
all  the  values  of  km  are  collected  and  reduced  by  aid  of  this  formula  to  a  common 
mean  temperature  of  10°  C. ;  the  values  refer,  also,  to  a  mean  barometric  pressure 
of  736  mm.  An  additional  column  is  added,  giving  the  corresponding  value  of 
k  in  English  measures  for  velocities  expressed  in  feet  per  second  and  pressures  in 
pounds  per  square  foot. 

TABLE    XVIII. 

Summary  of  values  of  km  obtained  with  the  Rolling  Carriage. 


Size  of  plane. 

Date. 

Number 
of 
observa- 
tions. 

Tempera- 
ture 
C°. 

Km< 

Km) 

for  t  =  10°  C. 

*, 

for<=10°C. 

12  inches  square. 

6  inches  square. 
8  inches  square. 

1888. 
Oct.,  24 
"      30 
Nov.    2 

1890. 
Nov.  28 

1888. 
Oct.   24 
"      29 
Nov.    1 
2 

Oct.   26 

9 
11 

4 

3 

3 
6 
12 
13 

7 

10.0 
7.8 
19.0 

-    2.0 
Weighted  i 

10.0 
12.0 
20.0 
19.0 

Weighted  i 

16.0 
General  we 

0.01027 
0.00913 
0.00830 

0.00990 
nean  

0.01027 
0.00906 
0.00859 

0.00948 

0.00180 

0.00159 

0.00147 
0.00166 

0.00944 

0.00760 
0.00785 
0.00810 
0.00840 

nean  

0.00760 
0.00790 
0.00840 
0.00867 

0.00833 

0.00770 
0.0087 

0.00754 
sighted  mean. 

THE    ROLLING   CARRIAGE. 

The  resulting  values  of  km  for  the  6,  8,  and  12  inch  square  planes  are  not 
entii-ely  accordant,  as  the  successive  sets  of  observations  with  the  12-inch  plane 
all  give  considerably  larger  values  than  those  obtained  with  the  smaller  planes. 
I  am  not  disposed,  however,  to  consider  this  as  a  real  effect  due  to  an  actual 
difference  in  the  pressure  per  unit  area  on  these  planes.  Such  a  difference,  if  one 
exists,  is  in  all  probability  quite  small,  and  much  within  the  degree  of  accuracy 
possessed  by  these  experiments.  The  resulting  differences  in  the  mean  values  of 
km  I  consider,  therefore,  as  discrepancies  in  the  observations,  the  cause  of  which 
has  not  become  apparent.  In  recognition,  however,  of  the  fact  that  other  experi- 
menters have  claimed  to  discover  a  difference  in  the  pressure  per  unit  area  on 
planes  of  different  sizes,  I  have,  in  general,  in  the  preceding  chapters,  taken  pains 
to  specify  the  area  of  the  plane  to  which  all  my  experimental  results  apply. 
That  there  should  be  a  real,  though  perhaps  a  small,  difference  between  the 
pressure  per  unit  area  on  planes  of  different  sizes  seems  in  fact  quite  probable, 
when  we  consider  that  the  ratio  of  perimeter  to  area  varies  for  similar  shaped 
planes  of  different  sizes.  If  the  side  of  a  square  plane  be  a  and  that  of  another 

4  4 

be  na,  the  ratio  of  perimeter  to  surface  is  -  in  the  one  case  and  —  in  the   other, 

which  is  not  merely  an  expression  of  a  mathematical  relation,  but  calls  attention 
to  a  possibly  important  physical  fact,  for  it  seems  probable  that  this  relation 
between  perimeter  and  area  has  a  considerable  influence  in  determining  the 
pressure  on  the  plane,  especially  that  part  of  it  produced  by  the  diminution  of 
pressure  on  its  posterior  face. 

The  general  weighted  mean  of  all  the  values  of  km  is  .0087,  or,  in  English 
measures,  k*=  .00166,  and  I  believe  this  result  is  within  10  per  cent,  of  the  true 
value.  These  experiments  lead  me  to  place  the  limits  of  the  value  of  km  for  a 
1-foot  square  plane,  between  0.0078  (k  =  .0015)  and  0.0095  (k  =  .0018)  for  the 
assumed  temperature  of  10°  C.,  and  pressure  736  mm.,  and,  made  as  they  were 
in  the  open  air  and  subject  to  wind  currents,  they  are  not  sufficiently  precise  to 
give  more  contracted  limits.  It  may  be  noted  that  the  value  of  km  obtained  from 
the  experiments  with  the  Resultant  Pressure  Recorder,  viz.,  km  —  .0080,  falls 
between  the  probable  limits  above  assigned,  and  is  within  the  probable  uncertainty 
(10  per  cent.)  of  the  mean  of  the  results  with  the  Soiling  Carriage.  The  Boiling 
Carriage,  therefore,  although  a  very  sensitive  and  delicate  piece  of  apparatus,  has 
not  been  able  under  the  conditions  of  experiment  to  yield  a  sensibly  better 
result  than  the  rougher  instrument. 

*Note  to  Second  Edition,  k  here  is  the  total  effect  of  pressure  before,  and  suction  behind,  and  has  the 
same  meaning  as  Newton's  resistentia  (Principia  Prop.  XXXVII).  It  is  the  total  effect  of  a  wind  of  1  foot 
per  second  on  1  square  foot.  A  velocity  of  1  foot  per  second  is  gained  by  falling  in  vacuo  from  a  height 
h  =  0  '-.0155  and  the  weight  of  a  column  of  air  of  this  height  and  1  square  foot  in  base  is  0Ibs'. 00128 
which  is  what  the  so-called  Newtonian  theorem  gives  as  the  value  of  the  pressure  on  the  front  face.  To  get 
the  total  resistance  (always  greater)  this  must  be  multiplied  by  some  factor  K  In  this  case  the 

1  £     ^    •       -00166  -     1    <m 

value   of  K  is 


100  EXPERIMENTS    IN    AERODYNAMICS. 

Measurement  of  wind  pressure  on  normal  planes  by  means  of  the  Rolling  Carriage. 

OCTOBER  24,  1888. 

PRESSURE  ON  ONE-FOOT  SQUARE  PLANE  (929  square  centimeters!. 
Barometer,  735  mm. ;  mean  temperature,  10° .0  C. ;  wind  velocity,  2.8  meters  per  second. 


1      <D 

<«    00 

60 

0 

-2:3 

°  <3 

a 

•rH 

Pressure  on  wind-plane. 

"J3 

2-2 

as  ID 

M   ^"~N 

1 

—  -      — 
t^K       C 

o      o 

it 

P 

(grammes 

,.          P 

*"•"•   T77 

«s 

<s  °'s 

-*"*'  c    ^ 

O 

•g'H 

(Pounds.) 

(Grammes.) 

per 

V 

I 

S  o  <3 

g-j3  5. 

O  r5     O) 

I1 

square 
centimeter). 

H 

* 

> 

1.20p.m.  '       14.00 

13.18 

3.39 

3.55 

1,610 

1.73 

0.0100 

r 

14.00 

13.18 

3.62 

3.84 

1,740 

1.87 

0.0108 

1.40  p.  m. 

9.49 

8.92 

1.42 

1.71 

776 

0.83 

0.0105 

r 

9.49 

8.92 

1.42 

1.71 

776 

0.83 

0.0105 

2.00  p.  m. 

5.50 

5.15 

0.32 

0.58 

263 

0.28 

0.0107 

f 

5.60 

5.28 

0.30 

0.53 

240 

0.26 

0.0093 

2.15  p.  m. 

14.90 

14.03 

3.90 

3.99 

1,810 

1.95 

0.0099 

'  15.00 

14.09 

4.10 

4.19 

1,900 

2.04 

0.0104 

14.80 

13.91 

4.00 

4.08 

1,850 

1.99 

0.0103 

Mean  = 

0.01027 

PRESSURE  ON  SIX-INCH  SQUARE  PLANE  (232  square  centimeters). 


| 

05    £3 

Jj 

|| 

•g  ^ 

Pressure  on  wind-plane. 

0 

o  ,3  oJ 

"c  P     • 

&1  S 

imeofobsen 

*I1 

h   Q  E 

0>  fl   ja 

•a  ° 

I.S'S 

elocity  of  ce 
plane  V  (i 
per  second) 

ll 

b 

(Pounds.) 

(Grammes.) 

P 

(grammes 
per 
square 
centimeter). 

,          P 

-  v* 

E-i 

^ 

> 

H 

4.00  p.  m. 

2.32 

24.3 

1.93 

2.18 

990 

4.26 

0.0072 

2.52 

23.8 

1.97 

2.22 

1,008 

4.34 

0.0077 

2.52 

23.8 

2.05 

2.29 

1,040 

4.48 

0.0079 

Mean  = 

0.0076 

THE    ROLLING   CARRIAGE. 


101 


OCTOBER  25,  1888. 

PRESSURE  ON  EIGHT-INCH  SQUARE  PLANE  (413  square  centimeters). 
Barometer,  738  mm. ;  mean  temperature,  16° .0  (L;  wind  velocity,  0.6  meter  per  second. 


g 

1-2 

11 

60 

Pressure  on  wind-plane. 

1 

8  "2  aj 

U^. 

&1T 

1 

-^  i"i 

o       *"O 

fll 

P 

p 

1 

o 

|§| 

tS« 

O  ^"^ 

(Pounds.) 

(Grammes.) 

(grammes 
per 

OJ 

a 

jj.s's 

-2UP, 

1  6 
f* 

square 
centimeter). 

H 

B 

> 

m 

4.30  p.  m. 

4.29 

13.14 

0.97 

1.30 

590 

1.43 

0.0083 

4.29 

13.14 

0.75 

1.10 

499 

1.21 

0.0070 

4.38 

12.93 

0.82 

1.15 

522 

1.26 

0.0075 

4.38 

12.93 

0.78 

1.12 

508 

1.23 

0.0074 

2.88 

19.60 

2.33 

2.55 

1,157 

2.80 

0.0073 

2.90 

19.50 

2.28 

2.51 

1,139 

2.76 

0.0073 

5.15  p.  m. 

2.45 

23.10 

3.76 

3.90 

1,770 

4.29 

0.0080 

Mean  = 

0.00754 

OCTOBER  29,  1888. 

PRESSURE  ON  SIX-INCH  SQUARE  PLANE  (232  square  centimeters). 
Barometer,  735  mm.;  mean  temperature,  12°.0  C.;  wind  velocity  at  1  p.  m.,  3.3  meters  per  second. 


§ 

1-2 

<o  g 

a 

Pressure  on  wind-plane. 

1 

Q>  "3  ^ 

l|x 

to  <o 

o> 

1 

•gil 

"s^  § 

fll 

P 
(grammes 

Km   rTTy 

IH 

O 

III 

£§  S 

'S1-1 

(Pounds.) 

(Grammes.) 

per 

V 

3  d  ^ 

§  6 

square 

g 

§.9*3 

'i'ftS, 

"S'z; 

centimeter). 

H 

S5 

> 

H 

4.24  p.  m. 

2.15 

26.30 

3.00 

3.20 

1,450 

6.25 

0.0090 

4.28  p.  m. 

2.03 

27.85 

3.08 

3.26 

1,480 

6.38 

0.0082 

4.33  p.  m. 

1.88 

30.15 

3.41 

3.57 

1,620 

6.98 

0.0077 

4.37  p.  m. 

1.93 

29.20 

3.19 

3.35 

1,520 

6.55 

0.0077 

5.29  p.  m. 

4.29 

13.20 

0.36 

0.61 

277 

1.19 

0.0068 

5.33  p.  m. 

3.95 

14.30 

0.50 

0.80 

363 

1.57 

0.0077 

Mean  = 

0.00785 

102 


EXPERIMENTS    IN    AERODYNAMICS. 


OCTOBER  30,  1888. 

PRESSURE  ON  ONE-FOOT  SQUARE  PLANE  (929  square  centimetere). 
Barometer,  739  mm. ;  mean  temperature,  7°.8  C. ;  wind  velocity,  — . 


GO    fi 
11 

11 

1- 

Pressure  on  wind-plane. 

1-2  « 

"d  S 

ft  $ 

«|| 

o       ^ 

V                     £3 

83  1 

P 

p 

0  ^  c 

Ox 

§^ 

(grammes 

J3  §  g 

•f§°° 

•I- 

(Pounds.) 

(Grammes.) 

per 

V 

1.9*3 

Wft 

r 

square 
centimeter). 

7.23 

7.84 

0.88 

1.20 

544 

0.586 

0.0095 

10.14 

5.58 

0.25 

0.50 

227 

0.244 

0.0079 

7.89 

7.17 

0.69 

1.01 

458 

0.493 

0.0096 

10.86 

5.22 

0.27 

0.51 

231 

0.249 

0.0092 

11.32 

5.00 

0.28 

0.52 

236 

0.254 

0.0102 

8.56 

6.62 

0.47 

0.75 

340 

0.366 

0.0084 

6.64 

8.51 

1.00 

1.30 

589 

0.634 

0.0088 

6.74  ' 

8.39 

1.00 

1.30 

589 

0.634 

0.0090 

6.30 

8.98 

1.33 

1.62 

734 

0.790 

0.0098 

6.20 

9.12 

1.34 

1.63 

739 

0.796 

0.0096 

5.93 

9.54 

1.27 

1.56 

707 

0.761 

0.0084 

Mean  = 

0.00913 

NOVEMBER  1,  1888. 

PRESSURE  ON  SIX-INCH  SQUARE  PLANE  (232  square  centimeters). 
Barometer,  741  mm. ;  mean  temperature,  20°.0  C. ;  wind  velocity,  1.5  meters  per  second. 


d 

.2 

1.2 

11 

tJD 

•  rH         • 

Pressure  on  wind-plane. 

1 

o  "t* 

£J    ^     ^) 

O>    (5 

"S  a^ 

g-J 

<3 

<°  >2 

Iff 

"Sa 

p 

o 
"8 

o  >->  < 

14     <P     S 

J  o3 

•s^f 

§J 

(Pounds.) 

(Grammes.) 

(grammes) 
per 

km  =  T/i 

CD 

O  r5     (B 

s  jS 

square 

1 

J.S<0 

|     ftft 

1 

centimeter). 

3.30  p.  m. 

4.35 

13.00 

1.60 

0.78 

356 

1.53 

0.0091 

4.32 

13.10 

1.43 

0.70 

320 

1.38 

0.0080 

3.99 

14.20 

2.19 

1.04 

472 

2.03 

0.0100 

4.00 

14.14 

2.07 

0.99 

449 

1.93 

0.0096 

4.00 

14.14 

1.60 

0.78 

356 

1.53 

0.0077 

3.96 

14.30 

1.58 

0.78 

354 

1.53 

0.0075 

5.64 

10.00 

0.64 

0.36 

163 

0.70 

0.0070 

5.67 

9.97 

0.61 

0.35 

159 

0.69 

0.0069 

5.40 

10.47 

0.80 

0.43 

197 

0.85 

0.0077 

5.51 

10.26 

0.69 

0.38 

174 

0.75 

0.0071 

7.93 

7.13 

0.30 

0.20 

91 

0.39 

0.0077 

5.25  p.  m. 

7.60 

7.44 

0.40 

0.25 

113 

0.49 

0.0089 

Mean  = 

0.00810 

THE    ROLLING   CARRIAGE. 


103 


NOVEMBER  2,  1888. 

PRESSURE  ON  SIX-INCH  SQUARE  PLANE  (232  square  centimeters). 
Barometer,  735.6  mm. ;  mean  temperature,  19°.0  C. ;  wind  velocity,  1.5  meters  per  second. 


d 

o 

11 

"SB 

jf. 

Pressure  on  wind-plane. 

i 

Hi 

11^ 

&? 

o> 
£ 

o 

•sl| 

ir§ 

P 

P 

(grammes 

p 
" 

o 

tj      O      e^ 

a  d  3 

-&'a>    OD 

•§•* 

(Pounds.) 

(Grammes.) 

per 

0 

rO      O    -fj 

|.a  o 

life 

|  ° 

square 
centimeter). 

11.00  a.  in. 

2.14 

26.40 

2.92 

3.11 

1,411 

6.08 

0.0087 

2.13 

26.55 

2.62 

2.85 

1,294 

5.56 

0.0079 

2.43 

23.30 

2.27 

2.52 

1,143 

4.92 

0.0091 

2.73 

20.70 

1.80 

2.10 

953 

4.10 

0.0096 

2.91 

19.40 

1.32 

1.67 

758 

.     3.26 

0.0087 

5.66 

10.00 

0.16 

0.45 

204 

0.88 

0.0088 

3.72 

15.20 

0.52 

0.90 

408 

1.76  . 

0.0076 

3.62 

15.60 

0.53 

0.91 

413 

1.78 

0.0073 

3.10 

18.20 

1.19 

1.54 

699 

3.01 

0.0091 

2.03 

27.85 

3.49 

3.63 

1,646 

7.09 

0.0091 

2.03 

27.80 

3.08 

3.27 

1,484 

6.38 

0.0083 

1.99 

28.40 

3.00 

3.19 

1,448 

6.22 

0.0077 

1.94 

29.10 

2.84 

3.04 

1,380 

5.93 

0.0070 

Mean  = 

0.0084 

PRESSURE  ON  ONE-FOOT  SQUARE  PLANE  (929  square  centimeters). 
Note :  Wind  too  high  for  best  results. 


o 
'•§ 

||    _ 

'o  £ 
j§  "8 

M 

«r-t 

Pressure  on  wind-plane. 

1 

£f  3 

IvE^ 

o      ^ 

1"! 

p 

1 

o 

°  ^  o 

'o^  g 

P'sS 

(grammes 

p 

~o 

§§S 

&a  * 

•i1^ 

(Pounds.) 

(Grammes.) 

per 

V 

S 

O  r2     « 

§  ° 

square 

1 

Is 

>  ftclH 

1 

centimeter). 

1.50p.m. 

2.27 

24.9 

2.28 

10.60 

4,810 

5.18 

0.0084 

2.34 

24.1 

1.92 

9.05 

4,105 

4.42 

0.0076 

2.90 

19.5 

1.28 

6.25 

2,835 

3.05 

0.0080 

3.10 

18.2 

1.27 

6.20 

2,810 

3.03 

0.0092 

Mean  = 

0.0083 

104  EXPERIMENTS    IN    AERODYNAMICS. 

NOVEMBER  28,  1890. 

PRESSURE  ON  ONE-FOOT  SQUARE  PLANE  (929  square  centimeters). 
Barometer,  737  mm. ;  mean  temperature,  —  2°.0  C. ;  wind  velocity,  1.2  meters  per  second. 


o 

1 
I 

IL 

S  £3 

!t~ 

Jf 

•rH         " 

Pressure  on  wind-plane. 

p 

1 

•8 

b  S  E 

<u  G  3 
n  r~.  ^ 

|g| 

1- 

(Pounds.) 

(Grammes.) 

(grammes 
per 

p 

km=y, 

4> 

8  o  <** 

Or2     O 

®  >5 

square 

| 

|J   0 

^     &ft 

&3 

centimeter). 

4.8 

11.8 

2.60 

2.80 

1,270 

1.37 

0.0099 

5.0 

11.3 

2.40 

2.60 

1,179 

1.27 

0.0099 

4.9 

11.5   . 

2.48 

2.68 

1,216 

1.31 

0.0099 

I 

CHAPTER  X. 

SUMMARY. 

The  essential  feature  of  the  present  work  has  been  the  insistance  on  the 
importance  of  a  somewhat  unfamiliar  idea — that  rapid  aerial  locomotion  can  be 
effected  by  taking  advantage  of  the  inertia  of  the  air  and  its  elasticity.  Though 
the  fact  that  the  air  has  inertia  is  a  familiar  one,  and  though  the  flight  of  certain 
missiles  has  indicated  that  this  inertia  may  be  utilized  to  support  bodies  in  rapid 
motion,  the  importance  of  the  deductions  to  be  made  has  not  been  recognized. 
This  work  makes  the  importance  of  some  of  these  deductions  evident  by  experi- 
ment, and  perhaps  for  the  first  time  exhibits  them  in  their  true  import. 

This  memoir  is  essentially  a  presentation  of  experiments  alone,  without 
hypotheses,  and  with  only  such  indispensable  formulae  as  are  needed  to  link  the 
observations  together.  These  experiments  furnish  results  which  may  be  suc- 
cinctly summarized  as  follows: 

The  primary  experiment  with  the  Suspended  Plane  is  not  intended  per  se 
to  establish  a  new  fact,  but  to  enforce  attention  to  the  neglected  consequences  of 
the  fundamental  principle  that  the  pressure  of  a  fluid  is  always  normal  to  a 
surface  moving  in  it,  some  of  these  consequences  being  (1)  that  the  stress  neces- 
sary to  sustain  a  body  in  the  air  is  less  when  this  is  in  horizontal  motion  than 
when  at  rest ;  (2)  that  this  stress  instead  of  increasing,  diminishes  with  the 
increase  of  the  horizontal  velocity  (a  fact  at  variance  with  the  conclusions  of 
some  physicists  of  repute  and  with  ideas  still  popularly  held) ;  (3)  that  it  is  at 
least  probable  that  in  such  horizontal  flight  up  to  great  velocities  the  greater  the 
speed  the  less  the  power  required  to  maintain  it,  this  probability  being  already 
indicated  by  this  illustrative  experiment,  whi'e  demonstrative  evidence  follows 
later. 

The  experiments  which  are  presented  in  Chapter  IV  result  in  an  empirical 
curve,  giving  the  ratio  between  the  pressure  on  an  inclined  square  plane  and 
on  a  normal  plane  moving  in  the  air  with  the  same  velocity.  Incidentally  it 
is  shown  that  the  pressure  is  normal  to  the  inclined  surface,  and  hence  that  the 
effects  of  skin-friction,  viscosity,  and  the  like  are  negligible  in  such  experiments. 
It  is  also  shown  that  for  the  small  angles  most  used  in  actual  trial  of  the  plane,  the 
pressure  on  it  is  about  20  times  greater  than  that  assignable  from  the  theoretical 
formula  derived  from  Newton's  discussion  of  this  subject  in  the  Principia.  This 

14  (105) 


106  EXPERIMENTS    IN   AERODYNAMICS. 

last  experimental  result  is  not  presented  as  a  new  contribution  to  knowledge, 
since  it  had  previously  been  obtained  by  experimenters  in  the  early  part  of  this 
century  ;  but  as  their  results  appear  not  to  have  met  with  the  general  attention  or 
acceptance  they  deserve,  it  is  not  superfluous  either  to  produce  this  independent 
experimental  evidence  or  to  urge  its  importance. 

The  experiments  with  the  Plane-Dropper  introduce  matter  believed  to  be 
novel  as  well  as  important.  They  show  (1)  that  the  time  of  falling  of  a  hori- 
zontal plane  is  greater  when  moving  horizontally  than  when  at  rest,  and  (2)  that 
this  time  of  falling  most  notably  increases  with  the  velocity  of  lateral  translation  ; 

(3)  experiments  with  different  horizontal  planes  show  that  this  increase  in  the  time 
of  falling  is  greater  for  those  planes  whose  extension  from  front  to  back  is  small 
compared  with  their  length  measured    perpendicular  to  the  line  of  advance , 

(4)  the  horizontal  velocities  are  determined  at  which  variously  shaped  inclined 
planes  set  at  varying  angles  can  soar — that  is,  just  sustain  their  own  weight  in 
the  air  under  such  circumstances — and  these  data  afford  the  numerical   basis 
for  the  important  proposition  that  the  power  required  to  maintain  the  horizontal 
motion  of  an  inclined  aeroplane  is  less  for  high  speeds  than  for  low  ones  ;  (5)  by 
experiments  with  double  planes,  one  above  the  other,  it  is  shown  that  planes  of 
the  advantageous  shape  mentioned  above,  do  not  interfere  with  each  other  at. 
specified  speeds,  if  so  placed  at  an  interval  not  less  than  their  length  from  front 
to  back  ;  and  it  is  pointed  out  that  an  extension  of  this  method  enables  us  to 
determine  the  extent  to  which  any  underlying  air  stratum  is  disturbed  during 
the  plane's  passage. 

Chapter  VI  contains  further  data,  which  confirm  the  important  conclusions 
derived  from  the  experiments  with  the  Plane- Dropper,  already  cited,  and  some 
results  on  the  pressures  on  inclined  planes  having  different  "  aspects"  with  refer- 
ence to  the  direction  of  motion  are  also  presented,  which  are  believed  to  be  new 
and  of  importance.  Further  chapters  present  experiments  with  a  special  instru- 
ment called  the  Dynamometer-Chronograph  and  with  other  apparatus,  which 
give  data  regarding  aerial  propellers,  a  series  of  experiments  on  the  center  of 
pressure  of  moving  planes,  and  another  series  upon  the  pressure  on  a  normal 
plane. 

The  conclusions  as  to  the  weights  which  can  be  transported  in  horizontal 
flight  have  included  the  experimental  demonstration  that  the  air  friction  is 
negligible  within  the  limits  of  experiment.  It  has  not  been  thought  necessary 
to  present  any  evidence  that  an  engine  or  other  adjunct  which  might  be  applied 
to  give  these  planes  motion,  need  itself  oppose  no  other  than  frictional  resist- 
ance, if  enclosed  in  a  stream-line  form,  since  the  fact  that  such  forms  oppose 
no  other  resistance  whatever  to  fluid  motion,  has  been  abundantly  demonstrated 
by  Froude,  Rankine,  and  others. 


SUMMARY. 


107 


The  most  important  general  inference  from  these  experiments,  as  a  whole, 
is  that,  so  far  as  the  mere  power  to  sustain  heavy  bodies  in  the  air  by  mechanical 
flight  goes,  such  mechanical  flight  is  possible  with  engines  we  now  possess,  since 
effective  steam-engines  have  lately  been  built  weighing  less  than  10  pounds  to 
one  horse-power,  and  the  experiments  show  that  if  we  multiply  the  small  planes 
which  have  been  actually  used,  or  assume  a  larger  plane  to  have  approximately 
the  properties  of  similar  small  ones,  one  horse-power  rightly  applied,  can  sustain 
over  200  pounds  in  the  air  at  a  horizontal  velocity  of  over  20  meters  per  second 
(about  45  miles  an  hour),  and  still  more  at  still  higher  velocities.  These  numer- 
ical values  are  contained  in  the  following  table,  repeated  from  p.  66.  It  is  scarcely 
necessary  to  observe  that  the  planes  have  been  designedly  loaded,  till  they  weighed 
500  grammes  each,  and  that  such  a  system,  if  used  for  actual  flight,  need  weigh 
but  a  small  fraction  of  this  amount,  leaving  the  rest  of  the  sustainable  weight 
indicated,  disposable  for  engines  and  other  purposes.  I  have  found  in  experiment 
that  surfaces  approximately  plane  and  of  iV  this  weight  are  sufficiently  strong  for 
all  necessary  purposes  of  support. 

Data  for  soaring  of  30  x  ^.,8  inch  planes;  weight,  500  grammes. 


Angle    with 
horizon  «. 

Soaring  speed  F. 

Work  expended  per  min- 
ute. 

Weight  with  planes  of  like 
form  that  1  horse-power 
will  drive  through  the 
air  at  velocity  V.  * 

Meters  per 
second. 

Feet  per  sec- 
ond. 

Kilogram- 
meters. 

Foot-pounds. 

Kilo- 
grammes. 

Pounds. 

45 
30 
15 

11.2 

10.6 
11.2 

36.7 
34;8 
36.7 

336 
175 
86 

2,434 
1,268 
623 

6.8 
13.0 
26.5 

15 
29 
58 

10 

12.4 

40.7 

65 

474 

34.8 

77 

5 

15.2 

49.8 

41 

297 

55.5 

122 

2 

20.0 

65.6 

24 

174 

95.0 

209 

^Footnote  to  Second  Edition.  If  this  last  statement  had  not  been  misunderstood,  it  would  seem  super- 
fluous to  say  that  it  refers  not  to  an  actual  flying  machine,  with  the  limitations  on  speed  imposed  in  con- 
struction by  guys,  framing,  etc.,  and  by  the  loss  in  transmission  of  horse-power  between  that  generated  in 
the  engine  and  that  delivered  in  thrust-speed.  It  refers  to  the  ideal  condition  of  the  frictionless  plane,  as 
closely  determined  by  the  foregoing  experiments. 

These  remarks  are  also  to  be  borne  in  mind  in  interpreting  the  following  formula,  which  is  only  a  sum- 
mary of  results  given  elsewhere  in  the  book. 

From  the  fundamental  formulae  on  page  60,  if  the  weight  Wbe  one  pound;  the  area  A  one  square  foot, 
then  the  velocity  Kat  which  the  normal  movement  of  the  plane  is  constant  will  equal  nearly  24^  feet  per 
second  (where  k  [experimentally  determined]  equals  0.00166).  If  from  this  we  pass  to  the  more  extended 
case  where  the  plane  is  no  longer  normal  but  inclined  at  an  angle  a,  and  F  (a)  is  supposed  to  be  of  the  form 

2  sin  a 
1  _i_  S;n2  a>  then  using  the  foot,  pound,  second   units  we  have  the  following   formula   for   the   horse  power 

required  to  propel  an  aerodrome  supported  by  thin  frictionless  planes: 

Energy  expended  =  R  K/but  from  page  60  we  have  \V  =  k  A  V2  F  (a.)  Cos  o,  .-. 


W 


A  F  (a)  Cos  a 


,  also  R  —  W  tan  a,  but  in  the  foot,  pound,      cond  system  of  units,  Horse  Power= 


550   > 


a  \  , 


W 


=  W  tan  a\ k  A  F  (a)  Cos  a  = 
550 


550  Cos''2  a  i/  AkF(a) 


If  for  the  planes  we  substitute  certain  curved  surfaces,  the  power  may  be  materially  less;  but  the  discus- 
sion of  this  part  of  the  subject,  as  well  as  that  regarding  the  frictional  resistances  caused  by  the  necessary 
framing,  etc.,  the  loss  of  power  between  the  engine  and  the  actual  delivered  thrust-speed  in  an  actual  machine, 
does  not  belong  to  the  present  volume. 


108  EXPERIMENTS    IN    AERODYNAMICS. 

I  am  not  prepared  to  say  that  the  relations  of  power,  area,  weight,  and 
speed,  here  experimentally  established  for  planes  of  small  area,  will  hold  for 
indefinitely  large  ones ;  but  from  all  the  circumstances  of  experiment,  I  can 
entertain  no  doubt  that  they  do  so  hold  far  enough  to  afford  assurance  that  we 
can  transport,  (with  fuel  for  a  considerable  journey  and  at  speeds  liigh  enough  to 
make  us  independent  of  ordinary  winds,)  weights  many  times  greater  than  that 
of  a  man. 

In  this  mode  of  supporting  a  body  in  the  air,  its  specific  gravity,  instead  of 
being  as  heretofore  a  matter  of  primary  importance,  is  a  matter  of  indifference, 
the  support  being  derived  essentially  from  the  inertia  and  elasticity  of  the  air  on 
which  the  body  is  made  to  rapidly  run.  The  most  important  and  it  is  believed 
novel  truth,  already  announced,  immediately  follows  from  what  has  been  shown, 
that  whereas  in  land  or  marine  transport  increased  speed  is  maintained  only  by 
a  disproportionate  expenditure  of  power,  within  the  limits  of  experiment  in  such 
aerial  horizontal  transport,  the  higher  speeds  are  more  economical  of  power  than  the 
lower  ones. 

While  calling  attention  to  these  important  and  as  yet  little  known  truths,  I 
desire  to  add  as  a  final  caution,  that  I  have  not  asserted  that  planes  such  as  are 
here  employed  in  experiment,  or  even  that  planes  of  any  kind,  are  the  best  forms 
to  use  in  mechanical  flight,  and  that  I  have  also  not  asserted,  without  qualification, 
that  mechanical  flight  is  practically  possiblefsince  this  involves  questions  as  to 
the  method  of  constructing  the  mechanism,  of  securing  its  safe  ascent  and  descent, 
and  also  of  securing  the  indispensable  condition  for  the  economic  use  of  the  power 
I  have  shown  to  be  at  our  disposal — the  condition,  I  mean,  of  OUT  ability  to  guide 
it  in  the  desired  horizontal  direction  during  transport, — questions  which,  in  my 
opinion,  are  only  to  be  answered  by  further  experiment,  and  which  belong  to  the 
inchoate  art  or  science  of  aerodromics,  on  which  I  do  not  enter. 

I  wish,  however,  to  put  on  record  my  belief  that  the  time  has  come  for 
these  questions  to  engage  the  serious  attention,  not  only  of  engineers,  but  of 
all  interested  in  the  possibly  near  practical  solution  of  a  problem,  one  of  the 
most  important  in  its  consequences,  of  any  which  has  ever  presented  itself  in 
mechanics ;  for  this  solution,  it  is  here  shown,  cannot  longer  be  considered  beyond 
our  capacity  to  reach.* 

*  Footnote  to  Second  Edition.  Since  the  preceding  lines  were  written  the  writer  has  demonstrated  that 
mechanical  flight  is  possible  by  actually  performing  it  with  steel  flying  machines  nearly  a  thousand  times 
heavier  than  the  air,  driven  by  steam,  and  employing  as  a  rule  curved  sustaining  surfaces.  These  machines, 
which  were  built  by  the  writer,  weighed  from  thirty  to  forty  pounds,  and  they  have  arisen  and  descended  in 
safety,  their  flight  being  limited  intentionally  to  distances  of  from  K  a  mile  to  ^  of  a  mile,  at  speeds  vary- 
ing from  20  to  30  miles  an  hour.  (See  Nature,  Vol.  54,  May  28,  1896.) 

The  "inchoate  art"  of  aerodromics  has  since  made  a  corresponding  progress,  and,  while  leaving  a  great 
deal  to  be  done,  it  is  believed  by  the  writer  that  the  time  is  now  very  near  when  human  beings  will  be  trans- 
ported at  high  velocities,  though  perhaps  at  first  under  exceptional  conditions  such  as  are  demanded  in  the 
irts  of  war  rather  than  of  peace. 


APPENDIX  A. 

I  append  here  the  results  of  some  additional  experiments  made  with  the  Plane- Dropper 
to  determine  the  law  of  falling  of  a  horizontal  plane  having  a  horizontal  velocity  of  transla- 
tion. It  will  be  recalled  that  the  preceding  data  given  in  the  chapter  on  the  Plane-Dropper 
show  only  the  total  time  of  falling  a  distance  of  four  feet,  and  that  we  cannot  determine 
from  it  the  law  of  fall,  unless  we  know,  in  addition,  the  relative  diminution  in  the  accelera- 
tion during  the  descent,  and  whether  at  the  end  of  the  fall  the  plane  has  attained  an 
approximately  constant  velocity.  For  high  horizontal  velocities  and  for  the  most  advan- 
tageous planes,  it  is  not  impossible  that  an  approximately  constant  velocity  is  reached  within 
the  four-foot  fall  of  the  Plane- Dropper.  In  order  to  obtain  these  additional  data,  I  placed 
electric  contacts  upon  the  Plane-Dropper  at  intervals  of  every  foot,  and  introduced  other 
modifications  into  the  method  of  experiment.  The  accuracy  with  which  it  was  necessary 
to  measure  the  relative  times  of  fall  through  successive  feet  precluded  the  further  use  of  the. 
stationary  chronograph  for  the  registration,  and  I  adapted  a  Konig  chronoscope  to  this 
purpose. 

This  chronoscope  consists  of  a  tuning-fork  of  low  pitch,  which  is  made  to  vibrate  by 
the  action  of  an  electro-magnet.  The  vibrations  are  registered  by  a  pen-point  on  a  strip  of 
paper  covered  with  lamp-black,  which  is  passed  over  a  roller  during  the  time  of  fall.  A 
second  pen-point  worked  by  an  electro-magnet  records  the  passage  of  the  falling-piece  over 
the  five  successive  contact-pieces  of  the  Plane-Dropper.  On  the  same  strip,  therefore,  we 
have  the  relative  intervals  between  the  successive  contacts,  and  a  time-scale  for  their 
evaluation.  Although  not  essential  for  the  evaluation  of  the  intervals,  approximate 
uniformity  in  the  motion  of  the  strip  of  paper  was  obtained  by  fastening  to  the  ends  brass 
clips  differing  suitably  in  weight,  and  converting  this  part  of  the  apparatus  into  an  Atwood's 
machine. 

Two  separate  batteries  were  used,  an  electropoion  battery  of  four  cells,  equivalent  to 
thirty  or  forty  Daniel's  cells,  for  vibrating  the  tuning-fork,  and  an  ordinary  battery  of  eight 
cells  for  the  Plane-Dropper  and  the  quadrant  contacts  of  the  turn-table.  The  current  from 
this  battery  is  forked  into  two  branches,  one  branch  running  to  the  quadrant  contacts  of  the 
turn-table  and  to  the  observatory  chronograph  on  which  they  register;  the  other  branch, 
going  to  the  Plane-Dropper,  actuates  the  release  magnet,  passes  through  the  five  electric 
contacts,  and  thence  goes  to  the  electro-magnet  on  the  Konig  chronoscope,  where  these 
contacts  are  registered,  and  finally  back  to  the  battery.  This  circuit  is  closed  by  a  make- 
key  in  the  hands  of  the  operator  at  the  chronoscope. 

A  preliminary  calibration  of  the  tuning-fork  was  made  by  connecting  one  pen  of  the 
chronoscope  with  the  mean  time-clock,  and  obtaining  a  number  of  strips  containing  both 
second  intervals  and  tuning-fork  vibrations. 

(109) 


110 


EXPERIMENTS    IN    AERODYNAMICS. 

Oalibration  of  tuning-fork. 

DECEMBER  12, 1890. — G.  E.  CURTIS,  Observer. 

Temperature  of  tuning-fork,  18°  C. 


Number  of 
strip. 

Number  of  vibrations  of  fork  per  second. 

1st  second. 

2d  second. 

Mean  of  2 
seconds. 

1 
3 
4 

5 

49.9 

48.6 
48.2 
47.8 
48.8 
48.6 
48.8 

51.9 

51.0 
50.8 

Mean,  49.9  vibrations  per  second. 

The  measurement  of  the  strips  showed  that  the  clock  was  not  "on  beat,"  and  that  two 
successive  seconds  must  be  taken  in  order  to  get  the  true  interval.  The  mean  of  the 
measurements  gave  49.9  vibrations  per  second.  The  tuning-fork  was  evidently  constructed 
to  give  50.0  vibrations  per  second,  and  this  value  was  therefore  adopted.  The  fraction  of 
a  vibration  can  be  accurately  estimated  to.  tenths ;  hence  the  instrument,  as  used  in  these 
observations,  gave  time  intervals  to  ^  part  of  a  second,  which  is  sufficiently  accurate  for 
the  purpose. 

Preliminary  experiments  were  made  with  the  Plane-Dropper  at  rest  indoors  for  the 
purpose  of  testing  the  new  contacts  and  the  Konig  registration  apparatus.  The  pair  of 
12  x  6  inch  planes  were  fastened  horizontally  to  the  falling  piece.  Then  the  observer,  with 
one  hand,  sets  in  motion  the  blackened  strip  on  the  Konig,  and  with  the  other,  immediately 
thereafter,  presses  the  make-key,  which  operates  the  release  magnet  of  the  Plane-Dropper. 
The  blackened  strip  containing  the  registration  is  then  passed  through  a  solution  of  shellnc 
and  ammonia,  by  which  the  trace  is  permanently  set. 

The  result  of  these  preliminary  experiments  is  as  follows : 

Time  of  fall  of  pair  of  12x6  inch  planes,  horizontal. 
DECEMBER  10, 1890.— G.  E.  CURTIS,  Observer. 


Observed  time  of 
fall  (seconds). 

Theoretical  time 
(in  vacuo). 

Difference. 

1st  foot                  •'•    - 

0.220 

0.250 

2d  foot 

0.110 

0.104 

+  .006 

3d  foot                 -         —   --- 

0.090 

0.080 

.010 

4th  foot 

0.080 

0.066 

+  .014 

Total  4  feet 

0.500 

0.500 

APPENDIX    A. 


Ill 


The  first  contact  is  not  at  absolute  rest,  but  a  fraction  (0.4  or  0.5)  of  an  inch  below  the 
position  of  rest ;  hence,  when  it  records,  the  plane  has  already  attained  a  small  velocity. 
To  this  is  due  the  fact  that  the  time  of  falling  the  first  foot,  which  is  registered  by  the  first 
and  second  contacts,  is  less  than  the  computed  time  in  vacua  by  .03  second.  At  least  this 
amount  should  therefore  be  added  to  the  observed  time  for  the  first  foot,  and  the  total  time 
will  be  0.53  seconds.  This  gives  a  total  retardation  of  0.03  seconds,  due  to  the  resistance  of 
the  air.  Attention  is  called  to  the  symmetrical  character  of  the  differences  between  the 
observed  and  the  computed  time  in  vacua,  showing  the  increasing  retardation  corresponding 
to  increasing  velocities  of  fall.  Being  assured  by  these  results  of  the  perfect  adaptation  of 
the  apparatus  to  secure  the  desired  data,  the  Plane-Dropper  was  placed  upon  the  whirling- 
table  December  13,  1890. 

When  the  whirling-table  has  attained  uniform  motion  at  the  speed  desired,  a  signal  is 
given  to  the  obseryer  seated  at  the  Konig  chronoscope  to  proceed  with  the  experiment. 
First,  by  a  break-key  he  cuts  out  for  a  moment  the  quadrant  contacts  as  an  evidence  on 
the  chronograph  sheet  of  the  time  of  the  experiment.  Second,  the  chronoscope  strip,  which 
has  previously  been  prepared  and  placed  upon  the  roller,  is  set  in  motion  by  the  release  of 
a  detent,  and  an  instant  later,  when  the  strip  has  gotten  fully  into  motion,  the  make-key  of 
the  Plane-Dropper  circuit  is  pressed,  releasing  the  falling  plane.  As  the  falling  plane  passes 
each  of  the  five  contact  pieces  the  circuit  is  completed,  and  registration  is  made  upon  the 
Konig  strip.  In  two  seconds  after  setting  in  motion  the  Konig  strip  the  experiment  is  at 
an  end.  The  strip  containing  the  record  is  then  passed  through  the  solution  of  shellac  and 
alcohol  for  setting  the  trace,  after  which  it  is  measured  at  leisure.  Meanwhile  a  new  strip 
is  placed  upon  the  chronoscope,  and  the  apparatus  is  in  readiness  for  another  trial. 

The  results  of  the  observations  covering  a  range  of  horizontal  velocity  from  6  to  26 
meters  per  second  (13.5  to  58.5  miles  per  hour)  are  contained  in  the  accompanying  table. 

To  find  the  times  of  falling  successive  feet  of  planes  having  a  lumzrmtal  velocity. 

DECEMBER  13,  1890. 
F.  W.  VERY,  G.  E.  CURTIS,  Observers. 

One  pair  12  x  6  inch  planes  horizontal ;   weight,  464  grammes  (1.02  Ibs.) ;   mean  temperature,  0°  C. ;   wind 
velocity,  1.85  meters  per  second. 

TIMES  OF  FALL  AT  DIFFERENT  HORIZONTAL  VELOCITIES. 


Horizontal 
velocity 
(meters  per 
second). 

At  rest. 

6.0 

11.9 

12.0 

12.1 

14.6 

14.4 

18.0 

22.1 

26.2 

1st  foot 

0218 

0314 

0284 

0389 

0429 

0834 

0448 

0678 

0930 

0600 

1440 

0962 

2dfoot  .-~ 
3d  foot--  

0.112 
0089 

0.120 
0094 

0.111 
0088 

0.125 
0105 

0.257 

0.205 
0213 

0.147 
0166 

0.202 
0360 

0.450 
0306 

0.220 
0340 

0.285 
0280 

0.303 
0399 

4th  foot  

0079 

0082 

0077 

0098 

0235 

0190 

0180 

0487 

Total,  4  feet— 

0.498 

0.610 

0.560 

0.717 

1487* 

0951 

1340 

2005 

2151 

*  Seriously  affected  by  wind. 


112 


EXPERIMENTS    IN    AERODYNAMICS. 
SUMMARY. 


Velocity  (meters 
per  second). 

Time  of  falling 
4  feet. 

Increase  over  time 
in  vacuo. 

0.0 

0.55 

0.05 

6.0 

0.72 

0.22 

12.0 

0.95 

0.45 

18.0 

1.34 

0.84 

22.0 

2.00 

1.50 

26.0 

2.15 

1.65 

The  time  of  falling  the  total  4  feet  increases  from  0.55  second,  when  the  plane  is  at 
rest,  to  2.15  seconds,  when  the  plane  has  a  horizontal  velocity  of  26  meters  per  second. 
Examining  the  time  of  falling  the  several  successive  feet,  it  will  be  seen  that  there  is  no 
uniformity  in  the  relative  times  in  which  the  several  distances  were  passed  over.  Only  the 
first  experiment  at  6  meters  per  second  shows  a  velocity  of  fall  continually  increasing  at  a 
diminishing  rate  as  the  circumstances  require.  The  remaining  four  experiments,  for  which 
a  complete  record  was  obtained,  show  decreasing  velocities  of  fall  in  a  part  or  all  of  the 
distance  after  the  first  foot.  These  anomalous  and  discordant  results  are  in  all  probability 
due  to  wind  currents  having  a  vertical  component,  which  vitiated  the  observations.  Thus 
the  completeness  of  the  apparatus  and  the  perfection  of  the  details  of  operations,  whereby 
an  accuracy  of  ^-J^  of  a  second  was  secured,  were  all  rendered  futile  by  the  uncontrolled 
conditions  under  which  the  experiment  was  unavoidably  conducted,  and  no  decisive  result 
was  added  to  those  already  summarized. 


APPENDIX  B. 

Mr.  G.  E.  Curtis  calls  my  attention  to  the  fact  that  the  conclusion  that  the  power 
required  to  maintain  the  horizontal  flight  of  an  aeroplane  diminishes  with  the  increasing 
speeds  that  it  attains,  may  be  deductively  shown  by  the  following  analysis : 

Representing  the  work  to  be  done  per  second  by  T,  the  resistance  to  horizontal  motion 
by  R,  and  the  horizontal  velocity  by  V,  we  have  by  definition 

T=  RV. 

Substituting  for  R  its  value,  W  tan  a  (see  p.  65),  W  being  the  weight  of  the  plane,  we 
have  the  equation 

T=  VWtana, 

in  which  a  and  V  are  dependent  variables.     The  curves  of  soaring  speed  (Fig.  9)  enable 
us,  in  the  case  of  a  few  planes,  to  express  «  in  terms  of  V,  but,  for  any  plane  and  without 
actually  obtaining  an  analytical  relation  between  Fand  «,  we  may  determine  the  character 
of  the  function  T,  i.  e.,  whether  it  increases  or  decreases  with  V,  in  the  following  manner : 
Differentiating  with  respect  to  V,  we  obtain 


—  W  (tana  +Vsec'a  j^J. 


Now,  since  in  flight  a  is  a  very  small  angle,  tan  a  will  be  small  as  compared  with  the 
term  V  sec2  a  ~-  Hence  the  sign  of  the  latter  factor  T-£  will  control  the  sign  of  •»-»- 

Now,  since  V  increases  as  a  diminishes,  -7-^.  is  negative,  which  makes  the  term  V  sec*  «  -f£ 

negative,  and  therefore,  in  general,  T  is  a  decreasing  function  of  V.  In  other  words, 
neglecting  the  skin  friction  and  also  any  end  pressure  that  there  may  be  on  the  plane,  the 
work  to  be  done  against  resistance  in  the  horizontal  flight  of  an  inclined  plane  must 
diminish  as  the  velocity  increases. 


(113) 


APPENDIX  C. 


At  the  time  of  my  experiments  to  determine  the  varying  position  of  the  center  of 
pressure  on  an  inclined  plane  moving  in  the  air,  I  was  unacquainted  with  the  similar 
experimental  work  of  Joessel  *  and  of  Kummer  f  in  the  same  field.  Joessel,  who  appears 
to  be  the  first  experimenter  on  the  subject,  found  for  a  square  plane  of  length  L  that,  as 
the  angle  between  the  plane  and  the  current  is  diminished,  the  center  of  pressure  approaches 
a  point  £  L  from  the  forward  edge,  and  that  its  position  for  any  angle  «  between  the  plane 
and  the  current  may  be  represented  by  the  formula 

d  =  (0.3  —  0.3  sin  a)  L, 

d  being  the  distance  of  the  center  of  pressure  from  the  center  of  plane. 

The  method  of  experiment  adopted  by  Kummer  is  essentially  similar  to  the  one  pur- 
sued by  me  in  the  use  of  the  Counterpoised  Eccentric  Plane.  The  object  is  to  determine  the 
position  of  the  center  of  pressure  corresponding  to  different  angles  of  inclination  of  a  plane 
to  the  current.  The  method  pursued  both  by  Kummer  and  myself  has  been  the  one  which 
most  naturally  suggests  itself  to  find  the  angle  of  inclination  a  of  the  plane  corresponding 
to  a  series  of  fixed  distances  d  of  the  center  of  pressure  from  the  center  of  figure.  Thus  in 
the  experiments,  d  has  been  the  independent  variable,  while  in  the  use  of  the  results,  «  is 
in  general  the  independent  variable. 

For  a  square  plane  90  mm.  (3.54  inches)  on  the  side,  Kummer  obtained  the  following 
results,  which  may  be  compared  with  the  results  given  here  in  chapter  VIII  and  with  the 
formula  of  Joessel : 


Distance  of  center 
of  pressure  from 
center  of  plane. 

Distance  as  a  per- 
centage of  side  of 
plane. 

Angle  of  plane  with 
current. 

mm. 

o 

0 

0.000 

90 

1 

0.011 

84 

2 

0.022 

77 

3 

0.033 

70 

4 

0.044 

62 

5 

0.056 

52 

6 

0.067 

41 

7 

0.078 

31 

8 

0.089 

28 

9 

0.100 

26 

10 

0.111 

25 

13 

0.144 

21 

14 

0.156 

19 

15 

0.167 

18 

*  Memorial  du  Ge'nie  Maritime,  1870. 
t  Berlin  Akad-Ahhandlungen,  1875,  187(i. 


(114) 


APPENDIX    C. 


115 


In  addition  to  determining  the  position  of  the  center  of  pressure  for  a  square  plane, 
Kummer  extended  his  experiments  to  the  case  of  differently  shaped  rectangles,  and  his 
results  with  these  are  strikingly  suggestive.  It  has  been  pointed  out  in  chapter  VI  that 
above  and  below  an  angle  of  about  30°  there  is  a  reversal  in  the  relative  amounts  of  the 
pressure  on  inclined  rectanglar  planes  of  different  shapes;  the  tabulated  results  of  Kummer 
exhibit  a  similar  reversal  in  the  position  of  the  center  of  pressure,  of  which  the  following 
may  be  given  as  an  example : 

Distance  of  center  of  pressure  from  center  of  plane. 


Size  of  plane. 

Angles  between  plane  and  current. 

45°. 

10°. 

mm. 
180  x  180 
90  x  180 

mm. 
11 
14 

mm. 
40 
36 

For  small  angles  the  position  of  the  center  of  pressure  is  further  from  the  center  of 
figure  in  the  180  x  180  mm.  plane  than  in  the  90  x  180  mm.  plane,  while  for  45°  this 
relation  is  reversed.  It  appears,  therefore,  that  the  reversal  in  the  amount  of  pressure, 
brought  out  in  the  experiments  presented  in  this  memoir,  finds  its  counterpart  in  a  corre- 
sponding reversal  in  the  position  of  the  center  of  pressure  exhibited  in  the  work  of  Kummer. 
It  is  believed  that  in  this  striking  analogy  may  be  found  a  key  to  the  more  complete 
rational  and  deductive  treatment  of  these  inseparably  related  problems. 


PLATE    T 


ALLEGHENY    OBSERVATORY. 


Flan  of  Grounds. 

SCALE:   1  INCH— -20  TEET 


PLAN    OF 


II 


ELEVATION  OF  WHI  RLI  NG  TABLE 


Designed  by  S.P.LANGLEV. 


SECTION  ON  LINE:  OP. 


Under  ground  Shaft  to  Cones  and  Engine 


LING   TABLE. 


OF  THE 

UNIVERSITY 

OF 


PLATE-  JIT 


Designed  by  S  .P.  LANGLETY 


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WIRE. 


ELEVATION. 


Wire  througti  Underground 
Cable  to  Chronograph.  &Battery. 


QUADRANT  CONTACTS  or  WHIRLING  TABLE 

SCALE    9         ,         ?         ,         *         ,         9         .         9         .         m 


12  INCHES. 


PLATE    IV 


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RESULTANT    PRESSURE    RECOF 


Designed  by  S.P  ]^ANGLEY. 


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COUNTERPOISED    ECCENTRIC    PLANE. 

SCALE. 


Designedly  S.P.LiAN OLE Y. 


IfC/BMT   OH  BACK  Or 


SECTION  or  PLANC 


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PLANE    DROPPER. 

Designed  by    S  .P.  L ANGL.EY. 


Arm  of  Whirling- Tabl 


Section  though  A-B. 

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Magnet. 


ELEVATION. 

SCALE. 


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COMPONENT  PRESSURE  F 


Designed  by  S.P.LA\<;i. 


SCALE  . 


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ELEVATION 


HORIZONTAL 

SECTION  ON  LINE  G-H 


OUTLINE  OF  KNIFE-EDGE, 
PIVOT  AND  BEARINGS. 


ADJUSTABLE  BEARING. 

D 


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ORDER 


PLATE    VII 


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POSITION  OF  ROLLING  G 


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SECTION  ON   LINE    A — B. 


CHRONOGRAPH . 


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INCHES. 


SIDE  ELEVATI 

ROLLING  CARRIAGE  &.  C. 


INCHES. 


SCALI 

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Designed  by    S.  I 


PLATE    IX 


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RECORDING  W    CYLINDER 


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